Question

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

`t=1.020s`

Explanation:

Given Equation:

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

Actually the given equation is the 2nd equation of motion

i.e.
`S =V_(i) t+0.5at^(2)`

where
`S=0` because the astronaut jumps on the earth

and initial velocity
`V_(i)=5`

to find time
`t`, put the given value of
`a=9.8m/s^(2)` in the given equation, we get

`5t-0.5(9.8)t^(2) =0\\t(5-4.9t)=0\\ \ dividing\ both\ sides\ by\ t\ we \ get\\ 5-4.9t=0\\4.9t=5\\t=(5)/(4.9)\\ t=1.020s`

it will take
`t=1.020s` to reach the ground if he jumps on the Earth