How to solve a Physics question

Step 1 Read Problem

A bullet is fired from a rifle with a horizontal velocity of 500 feet per second from a height of 16feet at the same time, another bullet falls out of the gun. without obstruction, which bullet will reach the ground first? how long will it take? At what velocity will it hit?

Step 2 Draw Diagram

Step 3 Identify Data

We will take the downward direction of motion as positive.

In the case of Bullet A

u_ah = Horizontal component of initial velocity u_a

u_av = Vertical component of initial velocity u_a

It is convenient to resolve the velocity into horizontal and vertical components as these can be then dealt with independently of each other.

similarly

v_ah and v_av are the horizontal and vertical components of final velocity v_a

In the case of bullet B there is no horizontal velocity component as the bullet is dropping vertically with no horizontal movement at all.

u_b = initial velocity bullet B

v_b = final velocity of bullet B

Step 4 Choose Equation

We choose to solve this problem by using the following equations of motion

v² = u² + 2 as

and

v = u + at

where v and u are the final and initial velocities of an object, a is the acceleration and s is distance traveled, t is time.

Step 5 Solve equation

Case of Bullet A

In this the horizontal component of velocity is of no consequence as it will not change at all, as there is no force acting on it ( in such problems we assume that there is no air resistance)

However, the vertical velocity will change due to the action of acceleration due to gravity.

We first use the equation v_av² = u_av² + 2 as

in this a = g = acceleration due to gravity = 32 ft/s²

u_av = 0 m/s as the bullet is fired out in the horizontal direction

v_av is what we want to determine

s = height = 16 ft

so v_av² = 0 + ( 2 x 32 x 16)= 32²

hence v_av = 32 ft/s

Now we use the other equation that is v_av = u_av + at

so t = (v_av – u_av) / a

or t = (32-0)/32 = 1 s

Case of Bullet B

here

v_b² = u_b² + 2as

v_b² = 0 + (2 x 32 x 16) = 32²

so v_b = 32 ft/s

t = (v_b - u_b)/a

= (32-0)/32 = 1 s

So both bullets will hit the ground with the same vertical velocity and will take the same time to reach the ground

As bullet A also has a horizontal velocity of 500 m/s

So the actual velocity of bullet A will be

v = (v_av² + v_ah²)^1/2 ( raising to the power of means taking the square root)

=(500² + 32²)^1/2