Question

Superman is flying 54.5 m/s when he sees

a train about to fall into a river 850 m
away. He reaches the train in 4.22 s.
What is his final velocity?

Answer 1

348.34 m/s. When Superman reaches the train, his final velocity will be 348.34 m/s.

To solve this problem, we are going to use the kinematics equations for constant aceleration. The key for this problem are the equations
`d=v_(0) t+(at^(2) )/(2)` and
`v_(f) =v_(0) +at` where
`d` is distance,
`v_(0)` is the initial velocity,
`v_(f)` is the final velocity,
`t` is time, and
`a` is aceleration.

Superman's initial velocity is
`v_(0)=54.5(m)/(s)`, and he will have to cover a distance d = 850m in a time t = 4.22s. Since we know
`d`,
`v_(0)` and
`t`, we have to find the aceleration
`a` in order to find
`v_(f)`.

From the equation
`d=v_(0) t+(at^(2) )/(2)` we have to clear
`a`, getting the equation as follows:
`a=(2(d-v_(0)t) )/(t^(2) )`.

Substituting the values:

`a=(2(850m-54.5(m)/(s).4.22s) )/((4.22s)^(2))=69.63(m)/(s^(2))`

To find
`v_(f)` we use the equation
`v_(f) =v_(0) +at`.

Substituting the values:

`v_(f) =54.5(m)/(s) +(69.63(m)/(s^(2)).4.22s)=348.34(m)/(s)`