Question

A ball is thrown towards a wall 10m away with a velocity of 40m/s. At what angle must it be thrown if it is to enter a hole on the wall at a height of 7m from the groundground, neglecting wind effects

Answer 1

Answer on Question #67146-Physics-Other

A ball is thrown towards a wall 10m away with a velocity of 40m/s. At what angle must it be thrown if it is to enter a hole on the wall at a height of 7m from the ground, neglecting wind effects?

Solution

We use the formulas for projectile motion:

$$x = v_0 t \cos \theta = 40 t \cos \theta = 10 \rightarrow t = \frac{1}{4 \cos \theta}$$ $$y = v_0 t \sin \theta - \frac{1}{2} g t^2 = 40 t \sin \theta - \frac{1}{2} (9.8) t^2 = 7$$ $$40 \frac{1}{4 \cos \theta} \sin \theta - \frac{1}{2} (9.8) \left(\frac{1}{4 \cos \theta}\right)^2 = 7$$ $$10 \tan \theta - \frac{1}{32} (9.8) (\tan^2 \theta + 1) = 7$$

The quadratic equation gives:

$$\tan \theta_1 = 0.747748 \rightarrow \theta_1 = 36.8{}^\circ$$ $$\tan \theta_2 = 31.9053 \rightarrow \theta_2 = 88.2{}^\circ$$

Answer: $36.8{}^\circ$ or $88.2{}^\circ$.

Answer provided by https://www.AssignmentExpert.com