You drop a softball from the roof of our school, a height of 15 meters. How long does it take for the ball to hit the ground?

1 Answer
Maxwell
Apr 13, 2017

#t = 1.75 s#

Explanation:

First before doing anything, write down all the knowns/givens.

Given
#x = 15 m#

#a = 9.8 m/s^2#

#v_o = 0 m/s#
#t = ?#

Why is #v_o#, initial velocity, zero? The question stem states a softball was dropped from a roof. When something is dropped , the moment it is dropped, its velocity is given to be zero. The acceleration due to gravity should be known, #9.8 m/s^2#.

We are going to use of the kinematic equations to solve for time.

#color(white)(aaaaaaaaaaaaaa)##x = v_ot + (1/2)at^2#

#color(white)(aaaaaaaaaaaaaa)#

Using what's given, plug in and cancel when possible. Then isolate to get (t) by itself. Solve.

  • #15m = cancel(v_ot)^0 + (1/2)(9.8 m/s^2)(t)^2#
  • #15m = (1/2)(9.8 m/s^2)(t)^2#
  • #(2/1)15m = cancel(2/1)*cancel(1/2)(9.8 m/s^2)(t)^2#
  • #2(15m) = (9.8m/s^2)t^2#

  • #(1/(9.8m/s^2))2(15m) = cancel(1/(9.8m/s^2))cancel(9.8m/s^2)t^2#

  • #(2*15m)/(9.8m/s^2) = t^2#

  • #sqrt((2*15m)/(9.8m/s^2)) = t#

Answer: #t = 1.75 s#

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