Answer to Question #293831 in Mechanical Engineering for wapwap

Question

A body is projected downward at an angle of 20° with respect to the horizontal(+X axis), from the top of a building 170 m high. Its initial speed is 40 m/s. (a) How long will it take before striking the ground?

Answer 1

The initial vertical velocity $= u \times sin 20^0 = 40\times sin 20^0 = 13.68 m/s.$

The vertical height given (h) = 170 meters

Using the formula $h = ut + \frac{1}{2} gt^2$

$170 = 40\times t + 4.9t^2$

Solving the quadratic equation, we get

t= 3.08 seconds.

The range is given by $x= u cos\theta * t$

$x= 40 * cos 20^0 * 3.08$

Solving,

$x=115.77$ meters.