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Chapter 3: Problem 11

Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops and reaches the ground in 3.50 \(\mathrm{s}\) , while Milada jumps horizontally with an initial speed of 95.0 \(\mathrm{cm} / \mathrm{s}\) . How far from the base of the cliff will Milada hit the ground?

Short Answer

Expert verified
Milada lands 3.325 meters from the base of the cliff.

Step by step solution

01

Identify Given Information

We know that Chirpy takes 3.50 seconds to fall and Milada jumps with an initial horizontal velocity of 95.0 cm/s (which is 0.95 m/s when converted to meters). We will use this information to find out how far from the base of the cliff Milada will land.
02

Calculate Vertical Fall Time for Milada

Since both Chirpy and Milada fall from the same height, Milada will also take 3.50 seconds to reach the ground. This time is important to find the horizontal distance.
03

Determine Horizontal Distance Traveled by Milada

The horizontal distance can be calculated using the equation: \[ x = v_x imes t \]where \( v_x = 0.95 \, \text{m/s} \) (Milada's horizontal speed) and \( t = 3.50 \, \text{s} \). Substitute the given values:\[ x = 0.95 imes 3.50 = 3.325 \, \text{meters} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Horizontal Velocity
Horizontal velocity refers to the constant speed and direction at which an object moves along a horizontal path. In projectile motion, the horizontal component of velocity remains unchanged throughout the motion, provided there is no air resistance.

When Milada jumps off the cliff, her horizontal velocity is given as 95.0 cm/s, which we convert to 0.95 m/s. This means every second, Milada moves 0.95 meters forward.
  • It doesn't change because no horizontal forces act on her after the jump.
  • The only forces at play affect the vertical motion, such as gravity.
Thus, to find how far she traveled horizontally, we multiply her constant horizontal speed by the time taken to reach the ground (which is the same time that Chirpy took to fall). This application of horizontal motion helps us determine the landing spot of Milada.
Free Fall
Free fall describes the motion of an object under the influence of gravitational force alone. During free fall, the only acceleration acting on an object is due to gravity, which is approximately 9.8 m/s虏 on Earth.

In the problem with Milada and Chirpy, although they start differently, both crickets undergo free fall once they are in motion.
  • Chirpy simply drops, relying purely on gravity to speed up.
  • Milada, despite an initial horizontal push, still experiences the same gravitational pull vertically.
The vertical descent is unaffected by how they move horizontally. Consequently, both crickets take 3.50 seconds to hit the ground after leaving the cliff, showcasing that horizontal motion has no impact on vertical fall time.
Physics Problem Solving
Physics problems, like the cliff-jumping crickets, often require us to blend multiple concepts together. Here's how we solve such a problem step by step.

  • First, identify what's given in the problem and what needs solving. Recognize both Milada's horizontal speed and the time to fall due to free fall.
  • Understand each concept used: separate the horizontal from vertical components, knowing they don't affect each other.
  • Apply relevant formulas: use the formula for horizontal distance, \(x = v_x \times t\), where \(x\) is the horizontal distance, \(v_x\) the horizontal velocity, and \(t\) the time taken in free fall.
  • Substitute the known values into the formula to find the unknown.
Performing these steps logically and methodically helps unravel complex physics scenarios, yielding clear solutions and understanding of the mechanics involved.

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Most popular questions from this chapter

In a test of a "g-suit," a volunteer is rotated in a horizontal circle of radius 7.0 \(\mathrm{m}\) . What must the period of rotation be so that the centripetal ncceleration has a magnitude of \((a) 3.0 g ?^{7}(b) 10 g ?\)

The radius of the earth's orbit around the sun (assumed to be circular) is \(1.50 \times 10^{8} \mathrm{km},\) and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in \(\mathrm{m} / \mathrm{s} ?\) (b) What is the radial acceleration of the earth toward the sun, in \(\mathrm{m} / \mathrm{s}^{2} ?\) (c) Repeat parts (a) and (b) for the motion of the planet Mercury (orbit radius \(=5.79 \times 10^{7} \mathrm{km}\) , orbital period \(=88.0\) days.

In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 90.0 \(\mathrm{km} / \mathrm{h}\) , to his enemy's car, which is going 110 \(\mathrm{km} / \mathrm{h}\) . The enemy's car is 15.8 \(\mathrm{m}\) in front of the hero's when he lets go of the grenade. If the hero throws the grenade so its initial velocity relative to him is at an angle of \(45^{\circ}\) above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance. Find the magnitude of the velocity both relative to the hero and relative to the earth.

A rocket is launched vertically from rest with a constant upward acceleration of 1.75 \(\mathrm{m} / \mathrm{s}^{2} .\) Suddenly 22.0 \(\mathrm{s}\) after launch, an unneeded fuel tank is jettisoned by shooting it away from the rocket. Acrew member riding in the rocket measures that the initial speed of the tank is 25.0 \(\mathrm{m} / \mathrm{s}\) and that it moves perpendicular to the rocket's path. The fuel tank feels no appreciable air resistance and reels only the force of gravity once it leaves the rocket. (a) How feels only the force of gravity once it leaves the rocket. (a) How fast is the rocket moving at the instant the fuel tank is jettisoned? (b) What are the horizontal and vertical componed by (i) a crew unk's velocity just as it is jetisoned as measured by (i) a crew member in the rocket and (ii) a technician standing on the ground? (c) At what angle with respect to the horizontal does the jettisoned fuel tank initially move, as measured by a crew member in the rocket and (ii) a technician standing on the ground? (d) What maximum height above the launch pad does the jettisoned tank reach?

Bang! \(\quad\) A student sits atop a platform a distance \(h\) above the ground. He throws a large firecracker horizontally with a speed \(v\) . However, a wind blowing parallel to the ground gives the fire- cracker a constant horizontal acceleration with magnitude \(a\) . This results in the firecracker reaching the ground directly under the student. Determine the height \(h\) in terms of \(v, a,\) and \(g\) . You can ignore the effect of air resistance on the vertical motion.
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