A ball is thrown horizontally from a height of and hits the ground with a speed that is three times its initial speed. What is the initial speed?
The initial speed of a ball is.
1) The final speed of a ball is three times its initial speed.
2) Height above the ground is, .
Using the equations of projectile motion, we can find the initial velocity of a ball.When the object is thrown in the horizontal direction, its vertical component of the velocity is zero. As it moves down, it gains speed. Using this information and the kinematic equations, we can calculate the initial speed.
Let the initial velocity of a ball is .
So, the horizontal velocity, of a ball is .
The initial vertical velocity of the ball is zero.
When the ball strikes the ground, it will have horizontal as well as vertical velocity. Let us assume that its vertical velocity when the ball is about to hit the ground is .
So, the final speed is the magnitude of the final velocity. Hence,
Now, use the kinematic equation for the final velocity in the vertical direction.
From equation (i), we can write that
Therefore, the initial velocity with which the ball was thrown is .
The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of . (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to , what is the smallest radius of curvature for the track that can be tolerated? (b) At what speed must the train go around a curve with a radius to be at the acceleration limit?
In Fig. 4-48a, a sled moves in the negative X direction at constant speed while a ball of ice is shot from the sled with a velocity relative to the sled. When the ball lands its horizontal displacement relative to the ground (from its launch position to its landing position) is measured. Figure 4-48b givesas a function of . Assume the ball lands at approximately its launch height. What are the values of (a)and (b)? The ball’s displacement relative to the sled can also be measured. Assume that the sled’s velocity is not changed when the ball is shot. What is whenis (c) and (d) 15.0 m/s?
During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. Figure 4-51 shows a cross section of Mt. Fuji, in Japan. (a) At what initial speed would a bomb have to be ejected, at angleto the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h=3.30km and horizontal distance? Ignore, for the moment, the effects of air on the bomb’s travel. (b) What would be the time of flight? (c) Would the effect of the air increase or decrease your answer in (a)?
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