Calculus question

Question

A ball is tossed up from a tower 50m above the ground. If the ball has an initial velocity of 30m/s, how long will it take to hit the ground if a = -9.81m/s^2.

 

Help!?

Answer 1

Find height y as a function of time t, set y = 0, and solve for t.

 

v(t) = ∫adt = -9.81t + v(0) = -9.81t + 30

 

y(t) = ∫v(t)dt = -9.81t²/2 + 30t + y(0) = -4.905t² + 30t + 50

 

0 = -4.905t² + 30t + 50

 

t ≅ -1.36 or 7.48 seconds

 

Since t must be positive, discard the negative solution.

 

t ≅ 7.48 seconds