Question

The function h(t) =-5t^{2}+3t+1 represents the height of an apple, in meters, `t` seconds after it is tossed straight up in the air.

How many seconds will it take for the apple to reach the ground?

Round to three decimal places if necessary.

Answer 1

To find when the apple will reach the ground, we need to find when the height of the apple is zero.

So, we set h(t) = 0 and solve for t:

-5t^2 + 3t + 1 = 0

Using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -5, b = 3, and c = 1.

Plugging in the values, we get:

t = (-3 ± sqrt(3^2 - 4(-5)(1))) / 2(-5)

Simplifying:

t = (-3 ± sqrt(49)) / (-10)

t = (-3 ± 7) / (-10)

t = 0.4 or t = 1.3

We discard the negative value since time cannot be negative, so the apple will reach the ground after approximately 1.3 seconds.

Therefore, it will take 1.3 seconds for the apple to reach the ground.

Hope this helped (: