A student throws a snowball in the z direction from the window of a train moving

Question

A student throws a snowball in the z direction from the window of a train moving in the x direction. The position of the train is given by the equation: x = 0 + V_o t + 1/2 alpha t^2 where V_o = your student number/10,000 m/s and the trains acceleration is your student number/100,000 m/s^2. If the velocity of the snowball relative to the train is V_s/t = 2 m/s in the z direction, and is thrown from a height of 5 m above the ground, a) What is the initial magnitude and direction of the snowballs velocity relative to the ground? b) What is the magnitude and direction of the snowballs acceleration relative to the ground? c) If the snowball is released from (x, y, z) = (0, 5, 0) at time = 0, where does it hit the ground?

Explanation / Answer

given

velocity of the train

vo = student number /10000 = 0453628/10000 = 45.36 m/s

, the initial velocity of hte snow ball relative to the ground is

vs/g= sqrt 2^2 + 45.36^2 = 45.4 m/s

direction theta = tan^-1 ( 45.4/2) = 87.47 degree

(b)

a= 0453628/100000 = 4.53 m/s^2

as/g = sqrt ( 4.53)^2 + (9.8)^2 = 10.79 /s^2

theta = tan^-1 ( 9.8/4.53 ) = 65.19 degree

(c)

Apply kinematic equation

s= vt + 1/2 at^2

5 = 1/2 ( 9.8) t^2

t = 1.01 s take to hit snow ball to the ground

x= ( -45.36) (1.01) + 1/2 ( 10.79) ( 1.01) ^2

x = -45.81 m

z= 2 ( 1.01) = 2.02 m

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