Question

A 1-kg model airplane has 12.5 joules of kinetic energy and 98 joules of gravitational potential energy. What is its speed? What is its height?

Answer 1

speed: `5` m/s
height: `9.99` m (3s.f.)

Explanation:

`KE = 1/2mv^2`
kinetic energy = `1/2` * mass * velocity squared

`12.5 J = 1/2 * 1kg * v^2`
`1 * v^2 = 25J`
`v^2 = 25J`
`v = +-5J`

since speed does not specify direction as velocity does, we can take the value of `5` m/s for speed.

`GPE = mgh`
gravitational potential energy = mass * gravitational field strength * height

assuming the airplane is flying above Earth, the gravitational field strength is `9.81`N/kg.

`98J = 1kg * 9.81J * h`

`98J = 9.81h`

`9.81h = 98`

`h = 98/9.81 = 9.99` (3s.f.)#

`h = 9.99`m (3s.f.)