Question

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 + 24.5t+9.8. Find the time it
takes for the cannonball to strike the ground.

Answer 1

• 5.4 seconds

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When the cannonball lands the height h is zero.

Set the value of the function as zero and solve for t:

• -4.9t² + 24.5t + 9.8 = 0
• t² - 5t - 2 = 0
• t = (5 ± √(5² + 8))/2
• t = (5 ± √33)/2
• t = (5 - √33)/2 or t = (5 + √33)/2
• t = - 0.4 or t = 5.4 (rounded)

The greater value of t represents the time we need.