If a certain cannon is fired from a height of 9.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h (t) = - 4.9t² + 30.5t + 9.8. Find the time it takes for the cannonball to strike the ground.

Question

Mathematics

Arielle Cannon

30 November, 22:42

If a certain cannon is fired from a height of 9.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h (t) = - 4.9t² + 30.5t + 9.8. Find the time it takes for the cannonball to strike the ground.

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Jerimiah Hansen · Answer 1

It will strike the ground when h (t) = 0 so

4.9t^2-30.5t-9.8=0

Since we have a bunch of decimals, I'll simply use the quadratic formula ...

t = (30.5±√1122.33) / 9.8, since t>0

t≈6.53 seconds