Consider two projectiles that can be shot upward by spring guns. Object A is mad

Question

Consider two projectiles that can be shot upward by spring guns. Object A is made of solid aluminum and has a mass of 50 grams. Object B is made of cast iron and has a mass of 200 grams. For this problem, you may take the gravitational field strength to be g = 10 N/kg and ignore the resistive forces of the air.

(a) Mass A is shot straight upward so that it exits the spring gun with a speed of 2.0 m/s. How high above the gun does it rise?
_________m

(b) Masses A and B are both shot straight upward at the same time. Mass A is shot with a speed of 2 m/s and mass B with a speed of 1 m/s. Which one hits the ground first?

A B Both at the same time or Cannot be determined from the information given.

(c) In the situation explained in case (b), which goes higher?

A B Both at the same time or Cannot be determined from the information given.

A B Both at the same time or Cannot be determined from the information given.

(e) Explain your reasoning.

Explanation / Answer

a)

V = speed = 2 m/s

h = height reached

m = mass

using conservation of energy

Kinetic energy = potential energy

(0.5) m V2 = mgh

h = V2 /(2g) = 22/(2 x 10) = 0.2 m

b)

For mass A :

Y = vertical displacement = 0

Vi = initial velocity = 2 m/s

t = time taken

a = acceleration = - 10 m/s2

Using the equation

Y = Vi t + (0.5) a t2

0 = 2 t + (0.5) (-10) t2

t = 0.4 sec

For mass B :

Y = vertical displacement = 0

Vi = initial velocity = 1 m/s

t = time taken

a = acceleration = - 10 m/s2

Using the equation

Y = Vi t + (0.5) a t2

0 = 1 t + (0.5) (-10) t2

t = 0.2 sec

So ball B takes less time

c)

Since the initial speed of ball A was greater , ball A goes higher as compared to ball B

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