Question

1. A body is launched upward at 30 m/s. After how much time is the object moving with half the initial speed, but in the downward direction to the nearest hundredth of a second?

2. A girl launches a ball straight up into the air on Earth. The average velocity of the ball from launch point until it attains its maximum height is 24 m/s. Ignore air resistance.

What is the maximum height above the launch point to the nearest tenth of a meter?

3. A body accelerates from rest at a rate of 7.0 m/s^2 for 6.5 seconds.

The body then accelerates at twice the rate as the first part for the same amount of time.

How far does the box travel during this entire motion to the nearest tenth of a meter?

Answer 1

1. At the highest point, final velocity, v = 0

Let t1 be the time taken to reach highest point, then, considering motion from launch to highest point and using, v = u + at, where, u = 30 m/s, v = 0, a = -9.8 m/s2, t = t1, we have,

0 = 30 - 9.8*t1 => t1 = 30/9.8 = 3.06 sec

For the motion from highest point until velocity becomes half the initial value, let t2 be the time taken, then, using, v = u + at, where,   v = 30/2 = 15 m/s, u = 0, a = 9.8, t = t2, we have,

15 = 0 + 9.8*t2 => t2 = 15/9.8 = 1.53 sec

So, required time = t1+t2 = (3.06+1.53) = 4.59 sec