An inquisitive physics student and mountain climber climbs a 47.0-m-high cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 2.08 m/s. (a) How long after release of the first stone do the two stones hit the water? (b) What initial velocity must the second stone have if the two stones are to hit the water simultaneously? magnitude m/s direction --Selectv (c) What is the speed of each stone at the instant the two stones hit the water? first stone m/s second stone m/s

In a local bar, a customer slides an empty beer mug down the slippery counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off of the counter and strikes the floor 2.11 m from the base of the counter. If the height of the counter is 1.62 m high, what is the magnitude of the velocity of the mug as it left the counter? Your Answer: Answer

Initially at rest, John catches a football at the 20 yard line, and immediately begins running forward with an acceleration of 2.3 m/s/s. At the instant John caught the ball, Bill (a player on the other team) happens to be 18.9 m away and he is running directly toward John at a constant 5.7 m/s. If the players run directly toward each other, then how far from the 20 yard line will Bill tackle John?

A rocket is fired at a speed of 83.0 m/s from ground level, at an angle of 45.0° above the horizontal. The rocket is fired toward an 12.5-m high wall, which is located 21.0 m away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall? Number i Units

A juggler throws balls straight up in the air. After the balls leave his hand and while it is in the air, explain WHY each of the following four statement is FALSE. Write the right answer. (a) The velocity of the ball is always in the same direction as it's acceleration. (b) The velocity of the ball is never in the same direction as it's acceleration. (c) The acceleration of the ball is zero. (d) The velocity of the pin is the same direction as it's acceleration on the way up.

Dock diving is great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.02 m/s at an angle of 25.0° with respect to the surface of the water. Sheba begins at a height of 0.840 m above the surface of the water. What is her total time of flight up until the instant before she hits the water? Express your answer in seconds.

A particle's position is given by  z(t) = −(7.30 m/s2)t2  for  t ≥ 0.  (Express your answer in vector form.) (a) Find the particle's velocity at  t = 2.50 s  and  t = 3.25 s. (b) What is the particle's average velocity during the time interval from  t = 2.50 s  to  t = 3.25 s?

Review Conceptual Example 15 before attempting this problem. Two identical pellet guns are fired simultaneously from the edge of a cliff. These guns impart an initial speed of 27.3 m/s to each pellet. Gun A is fired straight upward, with the pellet going up and then falling back down, eventually hitting the ground beneath the cliff. Gun B is fired straight downward. In the absence of air resistance, how long after pellet B hits the ground does pellet A hit the ground

The position of a particle along the positive x-axis is given by the following function r = 1t3 +14t2 +4, find the speed of the particle at time t=17, where t is in seconds and r is in cm.  Recall that the velocity can be found by taking the derivative of the position vector.  Express your answer in cm/s.

A person stands on a diving board and tosses a stone into a swimming pool. The stone is thrown from a height of 2.9 m above the water surface with a velocity of 2.8 m/s at an angle of 38° above the horizontal. As the stone strikes the water surface, it immediately slows down to exactly half the speed it had when it struck the water and maintains that speed while in the water. After the stone enters the water, it moves in a straight line in the direction of the velocity it had when. it struck the water. If the pool is 4 m deep, how much time elapses between when the stone is thrown and when it strikes the bottom of the pool? ttotal = S