Please correctly match each term.

A 3-kg object is dropped from a height of 5 m. The rock has an impact speed of...
A ball is rolled up a hill and comes to rest at a height of 10 m. Its original speed was about...
A ball is rolled up a hill with an initial speed of 3 m/s. To what height would it reach before coming to a stop.
A roller coaster needs to climb a tall hill. How tall of a hill can it climb with an initial sped of 15 m.s.
A child on a swing falls a height of 1m. What speed will the child reach?
A 1-kg toy car flies of a 1-m tall table at 2 m/s. Approximately what energy does it have when it strikes the floor?

12 joules
10 m/s
11.25 m
14.1 m/s
4.5 m/s
6.7 m

2 answers

These questions are all the same.
If there is no loss of energy of the system to heat or elsewhere the sum of potential and kinetic energy is constant
(1/2) m v^2 + m g h = constant
so for example
(1/2) m 0 ^2 + m (9.81) * 5= (1/2) m v^2 + m (9.81) * 0
or
(1/2)v^2 =9.81 * 5 [ note m does not matter if no change in mass]
v = sqrt (98.1) = 9.90 m/s
note if you used g = 10 the answer would be 10
by the way most of us try to remember that v= sqrt (2 g h)