An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance 𝑠 it travels and time 𝑡 is given by 𝑠=3𝑡+16𝑡2. How long does it take the object to fall 70 feet?It takes seconds for the object to fall 70 feet.
Question
An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance 𝑠 it travels and time 𝑡 is given by 𝑠=3𝑡+16𝑡2. How long does it take the object to fall 70 feet?It takes seconds for the object to fall 70 feet.
Solution
To find out how long it takes for the object to fall 70 feet, we need to set the equation for the distance s equal to 70 and solve for time t.
The equation given is s = 3t + 16t^2.
We set this equal to 70:
70 = 3t + 16t^2
Rearrange the equation to look like a standard quadratic equation (ax^2 + bx + c = 0):
16t^2 + 3t - 70 = 0
Now we can solve this quadratic equation for t using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)] / (2a):
t = [-(3) ± sqrt((3)^2 - 416(-70))] / (2*16)
t = [-3 ± sqrt(9 + 4480)] / 32
t = [-3 ± sqrt(4489)] / 32
t = [-3 ± 67] / 32
This gives us two possible solutions: t = 2 or t = -2.2.
However, time cannot be negative, so we discard the negative solution.
Therefore, it takes 2 seconds for the object to fall 70 feet.
Similar Questions
A ball is thrown vertically upward froma height of 40 m and hits the groundwith a speed that is three times itsinitial speed. What is the time taken (insec) for the fall (Take 𝑔 = 10 𝑚/𝑠2) ?
A body is thrown up with a velocity 40m𝑠-1. At same time another body is dropped from a height 40 m. Their relative acceleration after 1.3 seconds is
How long does it take a falling object (dropped from rest) to reach a downward velocity of 113 m/s?
(a)The function 𝑓(𝑡)=−5𝑡2+20𝑡+60f\left(t\right)=-5t^2+20t+60f(t)=−5t 2 +20t+60 models the approximate height of an object 𝑡tt seconds after it is launched. How many seconds does it take the object to hit the ground? (Enter only the number)
A parachutist's rate during a free fall reaches 65 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.Rate: ftsDistance fallen in 10 seconds: ft
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.