# Math Help - Finding the time it takes to hit the ground

1. ## Finding the time it takes to hit the ground

The ball is tossed up in the air from a tower 50m above the ground. If the ball has an inital velocity of 30m/s, how long will it take to hit the ground if a = -9.8m/s^2.

Now ive got my velocity function v = -10t +30, my height function h = -5t^2 +30t + 50, how can I find the total time?

Thank You!

2. First let us see what in formation we have:

s - Displacement - 50 metres
u - Initial velocity - 30m/s
v - Final velocity - N/A
a - Acceleration - 9.8m/s
t - Time - ?

We will take all values as downward, that is why we have acceleration as a positive value.

From the above information you should notice that we can use the following formula

$s = ut + \frac{1}{2}at^2$

Subbing in our values gives us,

$50 = 30t + 4.9t^2$

Which is just a normal quadratic.

Hope this helps

Craig

3. Originally Posted by Meeklo Braca
$h = -4.9t^2 + 30t + 50$