Question

ANSWER ASAP--Suppose an astronaut can jump vertically with an initial velocity of 5 m/s. The time that it takes him to touch the ground is given by the equation 0 = 5t - 0.5at2. The time t is in seconds and the acceleration due to gravity a is in m/s2. How long will it take him to reach the ground if he jumps on Earth where a = 9.8 m/s2?

Answer 1

It will take the astronaut 1.02 seconds to reach the ground.

Explanation:

If
`a = 9.8m/s^2`, then our equation becomes

`5t-0.5(9.8)t^2=0`

`5t-4.9t^2=0`

Add
`4.9t^2` to both sides and get

`5t = 4.9t^2`,

and dividing both sides by
`t`, we get:

`5 = 4.9t`

`$t = (5)/(4.9) $`

`\boxed{t = 1.02s}`

Therefore, it takes the astronaut 1.02 seconds to reach the ground.