# A body thrown vertically upward returns to the earth in three seconds.(a)what was the initial velocity of the body (b)what height did the body reach? Neglect air resistance.

##### 1 Answer

a 14.7 m/s

b 11 meters

#### Explanation:

A couple of facts we know. Gravitational acceleration in the vicinity of the earth's surface can be treated as a constant 9.81 m/s.

This is

With this, we can write a function for velocity v as a funciton of t:

(We are assigning a NEGATIVE value to downward acceleration & velocity)

We are given total flight time: 3 seconds.

So we know that at the halfway point (1.5 seconds), the ball will have reached maximum height, and v at that time will be 0.

The ball then accelerates downwards for the remaining 1.5 seconds.

Over this time it accelerates to

Since we're ignoring wind resistance, the downwards velocity at time t = 3 is equal in magnitude (opposite in direction) to the initial velocity. So this is your answer to part a: 14.7 m/s.

(I'm rounding to 3 significant digits in all arithmetic calculations).

We can then write an equation for the height, x, as a function of t:

At time t = 0, height x = 0, so our constant c is also 0.

Plugging in time t = 1.5, we can solve for the height at that time:

(once again, rounding to 3 significant digits.)