Homework Help: Projectile Motion, finding minimum speed

1. The problem statement, all variables and given/known data
A gazelle leaps over a 2.1m fence. Assuming a 45° takeoff angle, what is the minimum speed?


2. Relevant equations
1. x=v_0x * t
2. y = v_0y * t - 1/2gt²
3. v_y = v_0y - gt
4. v_y² = v_0y² - 2gΔy


3. The attempt at a solution
I assumed at the top of the leap, v_y=0 m/s, so I used equation 4 to find the initial y velocity (0m/s = v² - 2(9.8m/s²)(2.1m) which gave me v_y = 6.416 m/s)

I put the final y velocity into equation 3 to find t=0.6547 s.

Then I used 2.1m/tan 45° to find the x distance (2.1 m) and used that distance plus the time I found and plugged them into equation 1 to get the initial x velocity of 3.208 m/s.

Finally, I used the Pythagorean equation to find the actual initial velocity... The actual answer is 9.073 m/s, but I can't seem to work the problem out to that. I have a lot of problems with finding the initial minimum speed/velocity when given the final distances (even though I can find the range and maximum height when given the initial velocity) so any help would be greatly appreciated.

 

Right I got that it was the y velocity, and I tried to find the x component and do the Pythagorean equation... but I'm seeing now that the easiest thing to do is to use the y velocity/sin 45 to get the right answer.

Thanks.