# 1003 Return in 10 seconds | Rectilinear Translation

**Problem 1003**

A stone is thrown vertically upward and return to earth in 10 sec. What was its initial velocity and how high did it go?

**Solution**

Return in 10 seconds = 5 seconds upward + 5 seconds downward

Going upward (velocity at the highest point is zero):

$v_f = v_i - gt$
Going upward (velocity at the highest point is zero):

$v_f = v_i - gt$

SI Units

$v_f = v_i - gt$

$0 = v_i - 9.81(5)$

$v_i = 49.05 \, \text{ m/sec}$ *answer*

Going downward (initial velocity is zero; free-fall):

$h = \frac{1}{2}gt^2$

$h = \frac{1}{2}(9.81)(5^2)$

$h = 122.625 \, \text{ m}$ *answer*

English System

$v_f = v_i - gt$

$0 = v_i - 32.2(5)$

$v_i = 161 \, \text{ ft/sec}$ *answer*

Going downward (initial velocity is zero; free-fall):

$h = \frac{1}{2}gt^2$

$h = \frac{1}{2}(32.2)(5^2)$

$h = 402.5 \, \text{ ft}$ *answer*