A baseball approaches home plate at a speed of 43.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 54.0 m/s straight up. The ball has a mass of 145 g and is in contact with the bat for 2.30 ms. What is the average vector force the ball exerts on the bat during their interaction?

I tried calculating the vectors separately and then calculating the magnitude of both vectors added together but I'm not getting the correct answer.

Here is my work.

P initial = (0.145)(43)= 6.235
P final = (0.145)(54)=7.83

sq rt (7.83^2+6.235^2) = 10.0092

10.0092(0.0023)=4351.8 N

this is not correct?

6.235/.0023=2710i

7.83/.0023=3404j

= (2710)i-(3404)j

Because it's going against gravity @zain

It looks like you're on the right track, but you made a mistake when calculating the final momentum. Let's go through the correct calculation step by step to find the average vector force exerted on the bat.

First, let's calculate the initial momentum of the baseball. The initial velocity is 43.0 m/s, and the mass is 145 g or 0.145 kg.

P initial = mass x initial velocity
P initial = 0.145 kg x 43.0 m/s
P initial = 6.235 kg·m/s

Now, let's calculate the final momentum of the baseball. The final velocity is 54.0 m/s.

P final = mass x final velocity
P final = 0.145 kg x 54.0 m/s
P final = 7.83 kg·m/s

Next, we need to find the change in momentum during their interaction. The change in momentum is the difference between the final and initial momenta.

ΔP = P final - P initial
ΔP = 7.83 kg·m/s - 6.235 kg·m/s
ΔP = 1.595 kg·m/s

Now, we have the change in momentum. However, to find the average vector force, we need to divide this by the time of contact. The time of contact is given as 2.30 ms or 0.0023 s.

Average force = ΔP / Δt
Average force = 1.595 kg·m/s / 0.0023 s
Average force = 694.35 N

So, the average vector force the ball exerts on the bat during their interaction is 694.35 N.

To summarize the correct calculation:
1. Calculate the initial momentum: P initial = (0.145 kg) x (43.0 m/s) = 6.235 kg·m/s
2. Calculate the final momentum: P final = (0.145 kg) x (54.0 m/s) = 7.83 kg·m/s
3. Find the change in momentum: ΔP = P final - P initial = 1.595 kg·m/s
4. Divide the change in momentum by the time of contact to find the average force: Average force = ΔP / Δt = 694.35 N

why is the 3404 newtons negative?