Find the time it takes for the cannonball to strike the ground.

Question

If a certain cannon is fired from a height of 7.9 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+7.9. Find the time it takes for the cannonball to strike the ground.

Answer 1

We want to find the time, t, it takes for the cannonball to strike the ground. In other words, we need to solve the given equation for t.To do this, we must plug in the value for height, h, when the ball hits the ground, i.e. when the height, h = 0.

h(t)=−4.9t²+30.5t+7.9

0 = −4.9t² + 30.5t + 7.9

We can solve this using the quadratic equation, where a = −4.9, b = 30.5, and c = 7.9

t = [ −b ± √(b² - 4ac) ] / 2a

t = [ −30.5 ± √(30.5² - 4(−4.9)(7.9)) ] / 2(−4.9)

t = [ −30.5 ± √(930.25+154.84) ] / (−9.8)

t = [ −30.5 ± √(1085.09) ] / (−9.8)

t = [ −30.5 + √(1085.09) ] / (−9.8) OR t = [ −30.5 - √(1085.09) ] / (−9.8)

t = -0.249 OR t = 6.474

Because we want to know what happens after the cannon is fired (i.e., when time t >0), we can ignore the solution t = -0.249 seconds.

Therefore, the cannonball hits the ground (i.e. reaches height h = 0 m) after t = 6.474 seconds.

Answer 2

h(t) = -4.9t^2 +30.5t + 7.9 = 0

use the quadratic formula

t = -30.5/-9.8 + (1/9.8)sqr(30.5^2 +4(4.9)(7.9)

t= 6.4735 seconds

t = about 6 1/2 seconds to reach the ground