Question

A boy climbs to the roof of his house and throws a rock at a horizontal velocity of 11.5 m/s. The rock lands on the ground, 15.3 m from the base of the house. How high is the roof of the house?

Answer 1

The roof of the house is 8.67 m high

Step-by-step explanation:

Horizontal Motion

When an object is thrown horizontally with a speed v from a height h, the range or maximum horizontal distance traveled by the object can be calculated as follows:

`\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}`

The boy is on the roof of his house and throws a rock horizontally at v=11.5 m/s. It lands on the ground d=15.3 m from the base of the house. We can use the above equation to find the height of the roof by solving it by h:

`\displaystyle h=(gd^2)/(2v^2)`

Substituting values:

`\displaystyle h=(9.8\cdot 15.3^2)/(2\cdot 11.5^2)`

h=8.67 m

The roof of the house is 8.67 m high