In this problem, we are launching an object upward at an angle. Thus, this is a kinematics problem with a positive launch at an angle.

__CHAPTER 2: 1D KINEMATICS__

Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{-}}{\mathit{g}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}{\mathit{y}}_{\mathbf{0}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}{{\mathit{y}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{2}}{\mathit{g}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{-}}{\mathbf{2}}{\mathit{g}}{\mathbf{\u2206}}{\mathit{y}}}$

**a)**

We have horizontal distance from the wall = 24.0m.

Launch angle, θ = 53.0°

A playground is on the flat roof of a city school 6.00 m above the street below (Fig. P4.25). The vertical wall of the building is h = 7.00 m high forming a 1-m-high railing around the playground. A ball has fallen to the street below and a passerby returns it by launching it at an angle of u = 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.

(a) Find the speed at which the ball was launched.

(b) Find the vertical distance by which the ball clears the wall.

(c) Find the horizontal distance from the wall to the point on the roof where the ball lands.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Positive (Upward) Launch concept. You can view video lessons to learn Positive (Upward) Launch. Or if you need more Positive (Upward) Launch practice, you can also practice Positive (Upward) Launch practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Velissaris' class at UCF.