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Chapter 10: Q85P (page 293)

A golf ball is launched at an angle of $20 掳$ to the horizontal, with a speed of $60 m / s$ and a rotation rate of $90 \frac{rad}{s}$ . Neglecting air drag, determine the number of revolutions the ball makes by the time it reaches maximum height.

Short Answer

Expert verified

The number of revolutions the ball makes when at maximum height is $30$

Step by step solution

01

Given

Angle of launch is $20 掳$
Horizontal speed is $60 m / s$
Rotational rate is $90 \frac{rad}{sec}$

02

Understanding the concept

Find time to reach the maximum height using the kinematic equation. Using this time, find the angle in radians. The angle is nothing but angular displacement, which can be converted into a number of rotations using the relationship between one rotation and angle traced during one rotation.

Formula:

$v_{f y} = v_{0 y} + at$

$胃 - 胃_{0} = 蝇_{0} t$

03

Calculate the number of revolutions the ball makes by the time it reaches maximum height

Time to reach maximum height is as follows:

$v_{f y} = v_{0 y} + at$

At maximum height, the velocity is zero, so

$0 = 60 sin 20 - 9.8 t 鈬� t = 2.094 sec$

Now, the number of revolutions:

$胃 - 胃_{0} = 蝇_{0} t 鈬� 胃 - 胃_{0} = 90 脳 2.094 鈬� 胃 - 胃_{0} = 188 rad$

So

$188 脳 \frac{1 rev}{2 蟺} = 29.93 rev$

So, the number of revolutions is $30$ .

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Most popular questions from this chapter

If an airplane propeller rotates at $2000鈥塺别惫/尘颈苍$ while the airplane flies at a speed of $480km/h$ relative to the ground, what is the linear speed of a point on the tip of the propeller, at radius $1.5鈥尘$ , as seen by (a) the pilot and (b) an observer on the ground? The plane鈥檚 velocity is parallel to the propeller鈥檚 axis of rotation.

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In $5.0 s$ , it rotates $25 rad$ . During that time, what are the magnitudes of

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(b) the average angular velocity?

(c) What is the instantaneous angular velocity of the disk at the end of the $5.0 s$ ?

(d) With the angular acceleration unchanged, through what additional angle will the disk turn during the next $5.0 s$ ?

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The rigid object shown in Fig. $10-62$ consists of three ballsand three connecting rods, with $M =1.6kg, L =0.60m$ and $胃 = 30掳$ . The balls may be treated as particles, and the connecting rods have negligible mass. Determine the rotational kinetic energy of the object if it has an angular speed of $1.2鈥塺补诲/蝉$ about (a) an axis that passes through point P and is perpendicular to the plane of the figure and (b) an axis that passes through point P, is perpendicular to the rod of length $2L$ , and lies in the plane of the figure.

In Fig. $10 - 31$ , wheel A of radius $r_{A} = 10 鈥� cm$ is coupled by belt B to wheel C of radius $r_{C} = 25 鈥� cm$ .The angular speed of wheel A is increased from rest at a constant rate of $1.6 \frac{rad}{s^{2}}$ . Find the time needed for wheel C to reach an angular speed of $100 \frac{rev}{min}$ , assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)

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