Question

how to find final height in a work, kinetic energy problem with only the initial velocity, initial height and an angle? The object goes off a ramp with some projectile motion.

Answer 1

How to find final height in a work, kinetic energy problem with only the initial velocity, initial height and an angle? The object goes off a ramp with some projectile motion.

Answer

The increase of the height will last, until $v_{\mathrm{y}} = 0$.

$$0 = v _ {0} \sin (\alpha) - g t _ {h},$$

Time to reach the maximum height:

$$t _ {h} = \frac {v _ {0} \sin (\alpha)}{g}.$$

From the vertical displacement the maximum height of projectile:

$$h = v _ {0} t _ {h} \sin (\alpha) - \frac {1}{2} g t _ {h} ^ {2},$$

so

$$h = \frac {v _ {0} ^ {2} \sin^ {2} \alpha}{2 g}.$$