Question

Mark sees a crushed soda can on the ground. He kicks it fiercely with a velocity of 12m/s at projected angle of 36°. What is the highest point that the soda can reaches? Sin 36 degrees equals 0.866

Answer 1

Let's first find the time that the soda takes to reach its maximum height:

$$v_y=v_0sin\theta-gt,$$ $$0=v_0sin\theta-gt,$$ $$t=\dfrac{v_0sin\theta}{g}.$$

Finally, we can find the maximum height that the soda can reaches:

$$y_{max}=v_0tsin\theta-\dfrac{1}{2}gt^2,$$ $$y_{max}=v_0\dfrac{v_0sin\theta}{g}sin\theta-\dfrac{1}{2}g(\dfrac{v_0sin\theta}{g})^2,$$ $$y_{max}=\dfrac{v_0^2sin^2\theta}{2g}=\dfrac{(12\ \dfrac{m}{s})^2\cdot sin^236^{\circ}}{2\cdot9.8\ \dfrac{m}{s^2}}=2.54\ m.$$