A gazelle leaps over a 2.1m fence. Assuming a 45° takeoff angle, what is the minimum speed?
1. x=v0x * t
2. y = v0y * t - 1/2gt2
3. vy = v0y - gt
4. vy2 = v0y2 - 2gΔy
The Attempt at a Solution
I assumed at the top of the leap, vy=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 vy = 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.