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Chapter 2: Q. 59 (page 62)
A basketball player can jump to a height of 55 cm. How far
above the floor can he jump in an elevator that is descending at a constant 1.0 m/s?
The basketball player can jump at a height of above the floor in an elevator which is descending at a constant
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A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving at a speed of 400 m/s. What is the jet鈥檚 acceleration, assuming it to be a constant acceleration?
The Starship Enterprise returns from warp drive to ordinary
space with a forward speed of 50 km/s. To the crew鈥檚 great surprise,
a Klingon ship is 100 km directly ahead, traveling in the
same direction at a mere 20 km/s. Without evasive action, the
Enterprise will overtake and collide with the Klingons in just
slightly over 3.0 s. The Enterprise鈥檚 computers react instantly to
brake the ship. What magnitude acceleration does the Enterprise
need to just barely avoid a collision with the Klingon ship?
Assume the acceleration is constant.
Hint: Draw a position-versus-time graph showing the motions
of both the Enterprise and the Klingon ship. Let x0 = 0 km be
the location of the Enterprise as it returns from warp drive. How
do you show graphically the situation in which the collision is
鈥渂arely avoided鈥�? Once you decide what it looks like graphically,
express that situation mathematically.
FIGURE EX2.11 shows the velocity graph of a particle moving along the x-axis. Its initial position is x0 = 2.0 m at t0 = 0 s. At t = 2.0 s, what are the particle鈥檚 (a) position, (b) velocity, and (c) acceleration?
A rubber ball is shot straight up from the ground with speed v0. Simultaneously, a second rubber ball at a height h directly above the first ball is dropped from rest.
a. At what height above the ground do the balls collide? Your answer will be an algebraic expression in terms of h, v0, and g.
b. What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?
c. For what value of h does the collision occur at the instant when the first ball is at its highest point?
A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep.
a. What is the rock鈥檚 velocity as it hits the bottom of the hole?
b. How long is the rock in the air, from the instant it is released until it hits the bottom of the hole?
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