A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 17 m/s at an angle θ = 27 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position.

With what speed, vf in meters per second, does the stone strike the ground?

Question

Physics

Tanya Ramsey

29 May, 00:08

A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 17 m/s at an angle θ = 27 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position.

With what speed, vf in meters per second, does the stone strike the ground?

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Answers (1)

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Dominique Bean · Answer 1

The stone strikes the ground in 14.71m/s

Explanation:

The initial vertical velocity of the stone is given by:

Vyo = VSin theta

Given: V = 17m/s, theta = 27°

Vyo = 17 Sin 27

Vyo = 7.72m/s

Final vertical velocity, Vf can be determined by using kinematic equation

Vf^2 - U^2 = 2as

Vf^2 - (7.72) ^2 = 2 (9.8 * (-8))

Vf^2 = 59.60 + 156.8

Vf^2 = 216.4

Vf = sqrt (216.4)

Vf = 14.71m/s