Chapter 4, Problem 47A

Tiffany stands at the edge of a cliff and throws a ball straight up at a certain speed and another ball straight down with the same initial speed. Neglect air resistance.

a. Which ball is in the air for the longest time?

b. Which ball has the greater speed when it strikes the ground below?

To determine

The ball in the air for the longest time.

Answer to Problem 47A

A ball which was thrown up straight which certain speed is stays in air more than ball which is thrown downward from the edge of cliff.

Explanation of Solution

Given:

Ball-1 was thrown vertically upward with certain speed

Ball-2 was thrown downward with the same speed

Formula used:

Equation of motion is,

  $d=v_{0}t+\frac{1}{2}a{t}^2$

Ball-1 thrown upward so, it travels in upward direction from edge of cliff up to the point where its speed becomes zero and then its direction of motion is change to downward.

Assume that distance traveled by ball-1 from edge of cliff to top of its track is x. Hence ball 1 traveled distance 2x more than the ball-2.

Therefore, ball-1 stays in the air more than ball-2.

Conclusion:

A ball which was thrown up straight which certain speed is stays in air more than ball which is thrown downward from the edge of cliff.

To determine

The balls having greater speed just before it strikes with ground.

Answer to Problem 47A

Ball-1 which is thrown in upward direction has more velocity just before it strikes the ground.

Explanation of Solution

Given: Ball-1 was thrown vertically upward with certain speed

Ball-2 was thrown downward with the same speed

Formula used:

Equation of motion is,

  $v^2-v_0^2=2gd$ …(1)

Where,

  $v$ = Final speed of ball

  $v_0$ = Initial speed of ball

  $d$ = Distance traveled by the ball

Concept:

According to equation (1), if distance travelled by an object is more, its final velocity will also be more.

From part (a), the distance travelled by ball-1 is more. So, the final velocity of ball-1 will be more when it strikes the ground in comparison to ball-2.

Conclusion:

Ball-1 has more velocity just before it strikes with ground.