An object is launched from the ground. The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched. When will the object hit the ground after it is launched? Explain how you found your answer.
Answers
Given:
An object is launched from the ground.
The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched.
To find:
When will the object hit the ground after it is launched?
Solution:
From given, we have the equation of height of an object launched, given by,
h(t) = 80t – 16t2
When the object gets landed, height becomes 0, so we get,
h(t) = 0
⇒ 0 = 80t – 16t²
80t = 16t²
80 = 16t (t = 0, when launched)
t = 80/16
∴ t = 5 s.
The object hit the ground after it is launched in 5 seconds.
Answer: The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds.
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