Please make it clear and show where the numbers come from A man standing on the
ID: 1878130 • Letter: P
Question
Please make it clear and show where the numbers come from
A man standing on the ground throws a pebble with an initial velocity of 14 m/s at an angle of 70 degrees above the horizontal, hitting his friend's window 1.2 seconds later.
a) how high above the ground is the window?
b) how far from the building is the man standing in the horizontal direction?
c) What is the magnitude the velocity of the pebble when it hits the window?
d) What is the direction with respect to the horizontal of the velocity of the pebble when it hits the window?
e) Discuss whether or not your answers to parts a--d are reasonable.
Explanation / Answer
a)
Height h = v sin x t - 1/2 gt2
= 14 x sin(70) x 1.2 - 0.5 x 9.81 x (1.2)2
= 8.72 m
b)
Horizontal distance, R = v cos x t
= 14 x cos(70) x 1.2
= 5.75 m
c)
Initial vertical velocity = v sin
Velocity after time t = 1.2 s is
Vy = v sin - gt
= 14 x sin(70) - 9.81 x 1.2
= 1.38 m/s
Horizontal velocity remains constant, Vx = v cos
= 14 x cos(70)
= 4.79 m/s
Final velocity after 1.2 s is,
V = SQRT[Vx2 + Vy2]
= SQRT[1.382 + 4.792]
= 4.98 m/s
d)
tan = Vy/Vx
= tan-1(1.38/4.79)
= 16.12 degrees above horizontal