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This problem was given to me on a test today. I tried my best to figure it out but I'm still not sure, I did find a solution, I am just not sure if the solution is correct.
A long jumper jumps with an angle of 23 degrees and lands 8.59m away from the jump spot. What is the magnitude of the initial velocity of the jumper?
Assumptions:
The feet land in the same place as the body (the body is to be treated as an object)
Horizontal motion is constant
Given: (small "v" is speed, large "v" is velocity)
x - components
a = 0
Vi = vcos23
d = 8.59m
t = ?
y - components
a = 9.81m/s/s
Vi = vsin23
d = ? (assumed zero at landing)
t = ?
t = d/v
at = vf - vi
d = vi + 1/2at2
t = 8.59m / vcos23
from this point, I forgot explicitly the steps I took, but I subbed in what I knew for the initial velocities in an attempt to solve them. I ended up with:
-0.3907v2 -0.3907v + 91.2 = 0
I had included units in all my procedures, and the only units left in the equation were attached to the 91.2 and became m2s-2 (metres squared per seconds squared). I went on and used the quadratic formula anyway, despite the unit anomaly and came up with 14 m/s (rounded).
I am not sure if this is even remotely correct, and if I am not even on the right track, could anyone show me how to properly solve it? It seems I'm lacking a bit in the math department, though I am at the top of my physics class (top three anyway).
Homework Statement
A long jumper jumps with an angle of 23 degrees and lands 8.59m away from the jump spot. What is the magnitude of the initial velocity of the jumper?
Assumptions:
The feet land in the same place as the body (the body is to be treated as an object)
Horizontal motion is constant
Given: (small "v" is speed, large "v" is velocity)
x - components
a = 0
Vi = vcos23
d = 8.59m
t = ?
y - components
a = 9.81m/s/s
Vi = vsin23
d = ? (assumed zero at landing)
t = ?
Homework Equations
t = d/v
at = vf - vi
d = vi + 1/2at2
The Attempt at a Solution
t = 8.59m / vcos23
from this point, I forgot explicitly the steps I took, but I subbed in what I knew for the initial velocities in an attempt to solve them. I ended up with:
-0.3907v2 -0.3907v + 91.2 = 0
I had included units in all my procedures, and the only units left in the equation were attached to the 91.2 and became m2s-2 (metres squared per seconds squared). I went on and used the quadratic formula anyway, despite the unit anomaly and came up with 14 m/s (rounded).
I am not sure if this is even remotely correct, and if I am not even on the right track, could anyone show me how to properly solve it? It seems I'm lacking a bit in the math department, though I am at the top of my physics class (top three anyway).