Kinematics Word Problem - Projectile Fired at a Stationary Vehicle

[Wellesley1]

Homework Statement

A projectile is fired at a stationary vehicle. If the initial separation was 200m and the projectile traveled at a constant 75 m/s, find the acceleration the vehicle would need for a passenger to be able to reach out and calmly pull the projectile into the vehicle. (Assume the car starts accelerating at the same time as the projectile is fired). Let's say the projectile is a bullet.

Car:
vi = 0 m/s
vf = 75 m/s
a=?
d=?
t=?

Projectile:
vi= 75m/s
vf= 75m/s
a= constant so 0m/s
t=?
d=?

Homework Equations

d=v_it+1/2at₂

v²=v_i²+2ad

The Attempt at a Solution

So I've asked my physics teacher but he didn't really help. He's one of those stubborn teachers who you have focused on all your attention to him speaking. I'm not an auditory learner so I still don't understand how to solve this problem. I just need a push on how to solve the problem.

distance of bullet = 200m + distance of car

I've tried to use the d=vt+.5at^2 equation and have both the car and bullet's equation be t=t. I can't find an appropriate formula for the bullet.

 

[SammyS]

Homework Statement

A projectile is fired at a stationary vehicle. If the initial separation was 200m and the projectile traveled at a constant 75 m/s, find the acceleration the vehicle would need for a passenger to be able to reach out and calmly pull the projectile into the vehicle. (Assume the car starts accelerating at the same time as the projectile is fired). Let's say the projectile is a bullet.

Car:
vi = 0 m/s
vf = 75 m/s
a=?
d=?
t=?

Projectile:
vi= 75m/s
vf= 75m/s
a= constant so 0m/s
t=?
d=?

Homework Equations

d=v_it+1/2at₂

v²=v_i²+2ad

The Attempt at a Solution

So I've asked my physics teacher but he didn't really help. He's one of those stubborn teachers who you have focused on all your attention to him speaking. I'm not an auditory learner so I still don't understand how to solve this problem. I just need a push on how to solve the problem.

distance of bullet = 200m + distance of car

I've tried to use the d=vt+.5at^2 equation and have both the car and bullet's equation be t=t. I can't find an appropriate formula for the bullet.

Hello Wellesley1 . Welcome to PF !

How does the distance traveled by the bullet compare to the distance traveled by the vehicle ?

 

[rl.bhat]

The passenger can pull the projectile into the vehicle, when his velocity is equal the velocity of the projectile. That gives you one equation. Difference between the distances traveled by the projectile and the vehicle is given. That gives you the second equation. Solving these two equations, you can find the acceleration and the time.