Question

A bobsled slides down an ice track starting
(at zero initial speed) from the top of a(n)
174 m high hill.
The acceleration of gravity is 9.8 m/s
2
.
Neglect friction and air resistance and determine the bobsled’s speed at the bottom of
the hill.

Answer 1

You can use the kinematics equations to solve this, but it might be a little easier to start with the law of conservation of energy.
The potential energy at the top equals the kinetic energy at the bottom.
PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s/s) and h is height
KE is (1/2) m v^2, where m is mass and v is velocity

mgh = (1/2)m v^
mass cancels out
solve for \[ v = \sqrt{2gh}\]
the units are sqrt (m^2/s^s) which comes out to m/s so you know this is set up right

Or you could go with Vf^2 = vi^2 + 2as
where vf is the final velocity, vi is the initial velocity (zero in this case) a is acceleration, and s is displacement (or distance in this case) and you get the same solution as \[ vf =\sqrt{2as}\], (obviously replace a with g for the specific acceleration of 9.8 and s with h for height)