Projectile motion - solving for launch velocity

Question

A ball is hit at an initial velocity, 30° (above the horizontal) off a 20 m high cliff. Solve for the launch velocity given that the ball hits the ground at a speed of 25.1 m/s

Answer 1

There is more than one way to solve this problem.  I think that use of energy conservation is the easiest.  Have you seen that in your physics class?  If not, an alternative solution can be posted.

 

mgy₁ + mv_1y²/2 = mgy₂ + mv_2y²/2

 

y₁ = 20 m  [initial height]

v_1y = v sin30° = v/2  [v is what we want to solve for]

y₂ = 0 m  [final height when it hits the ground]

v_2y = 25.1 m/s  [I assume 25.1 m/s is the final VERTICAL speed when it hits the ground]

 

9.8(20) + (v/2)²/2 = 9.8(0) + (25.1)²/2

 

196 + v²/8 = 315.01

 

v = 30.86 m/s