P3: An object is launched from the top of a building with initial speed of 5 m/s

Question

P3: An object is launched from the top of a building with initial speed of 5 m/s. (a) If the object is launched at an angle of 30° above the horizontal and it takes 5 seconds to reach the ground, what is the height of the building, and what is the speed (magnitude of velocity only) right before it hits the ground. (b) If the object is launched at an angle of 30° below the horizontal and it takes 3 seconds to reach the ground, what is the height of the building, and what is the speed (magnitude of velocity only) right before it hits the ground. (e) If the object is launched horizontally and it takes 4 seconds to reach the ground, what is the height of the building, and what is the speed (magnitude of ground. velocity only) right before it hits the

Explanation / Answer

(a) in vertical,

v0y = 5 sin30 = 2.5 m/s

ay = - 9.8 m/s^2

y = yf - yi = 0 - h

y = v0y t + ay t^2 / 2

- h = (2.5 x 5) - (9.8 x 5^2 / 2)

h = 110 m

v^2 - 5^2 = 2(-110)(9.8)

v = 46.7 m/s

(b) v0y = -5 sin30 = -2.5 m/s

ay = - 9.8 m/s^2

y = yf - yi = 0 - h

y = v0y t + ay t^2 / 2

- h = (-2.5 x 3) - (9.8 x 3^2 / 2)

h = 51.6 m

v = 32.2 m/s

(c) v0y = 0

h = 9.8 x 4^2 / 2

h = 78.4 m

v = 39.5 m/s

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