7)

An apple falls from a tree (h = 9m). In the absence of air resistance,
how fast is it traveling when it strikes the ground?

Well, according to gravity, the apple should pick up quite some speed on its way down. But don't worry, it won't hit the ground with a moustache and a top hat, if that's what you're thinking! Ha! Anyway, the formula to calculate the speed of an object falling freely is given by: v = sqrt(2gh), where v is the velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the distance fallen (9m). So let's do the math: v = sqrt(2 * 9.8 m/s^2 * 9m) = sqrt(176.4 m^2/s^2) ≈ 13.3 m/s. So, when our apple reaches the ground, it will be traveling at approximately 13.3 meters per second. Just hope it doesn't go splat!

To calculate the speed at which the apple strikes the ground, we can use the equation for projectile motion:

v^2 = u^2 + 2gh

where:
- v is the final velocity of the apple when it strikes the ground
- u is the initial velocity of the apple (which in this case is 0 as the apple is initially at rest)
- g is the acceleration due to gravity (which is approximately 9.8 m/s^2)
- h is the height from which the apple falls (given as 9m)

Plugging in the values into the equation, we have:

v^2 = 0^2 + 2 * 9.8 * 9

Simplifying:

v^2 = 176.4

To find the final velocity, we can take the square root of both sides:

v = √176.4

v ≈ 13.3 m/s

Therefore, the apple is traveling at approximately 13.3 m/s when it strikes the ground in the absence of air resistance.

potential energy is mgh = m(9.8)(9) = 88.2m where m is the mass of the apple.

given that there is no air resistance, all of these potential energy is converted to kinetic energy during the fall

i.e. Ep = Ek

so, Ek = 1/2mv^2 = Ep

1/2mv^2 = 88.2m

v^2 = 88.2m/0.5m ...so you can solve for velocity.

hope that helps..