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How high can an animal jump if it can run at 20 m/s and leap from the ground with a vertical velocity of 5 m/s?
My reasoning:
I though that since KE is a scalar, you would use pythagorean theorem to find the velocity and plug that velocity into 1/2mv^2=mgh and you can find the maximum height from there.
EK says that you ignore the horizontal velocity and just take the vertical component of the velocity at 5 m/s and plug that into the kinematics equation v^2=2gh. I may be wrong, but this seems to directly conflict with TPR Physics example 5-23 which has a ball thrown with a velocity of 12 m/s and angle of 85 degrees. In this example, they took the 12 m/s and plugged it into KE=PE because kinetic energy is a scalar. If they used the reasoning of EK, they would plug 12sin85degrees m/s into the conservation of mechanical energy equation since this is the vertical component of the velocity. This problem asks for the final velocity at a particular height, instead of the maximum height, but it uses the same principles. If you run the problem the way I suggested with pythagorean theorem, you get 21.25 m, which is incorrect. For finding the maximum height with a projectile launched at an angle do I always just use the vertical component because I don't recall doing this before and I've never had a problem with this concept until now?
Answer: 1.25 m
My reasoning:
I though that since KE is a scalar, you would use pythagorean theorem to find the velocity and plug that velocity into 1/2mv^2=mgh and you can find the maximum height from there.
EK says that you ignore the horizontal velocity and just take the vertical component of the velocity at 5 m/s and plug that into the kinematics equation v^2=2gh. I may be wrong, but this seems to directly conflict with TPR Physics example 5-23 which has a ball thrown with a velocity of 12 m/s and angle of 85 degrees. In this example, they took the 12 m/s and plugged it into KE=PE because kinetic energy is a scalar. If they used the reasoning of EK, they would plug 12sin85degrees m/s into the conservation of mechanical energy equation since this is the vertical component of the velocity. This problem asks for the final velocity at a particular height, instead of the maximum height, but it uses the same principles. If you run the problem the way I suggested with pythagorean theorem, you get 21.25 m, which is incorrect. For finding the maximum height with a projectile launched at an angle do I always just use the vertical component because I don't recall doing this before and I've never had a problem with this concept until now?
Answer: 1.25 m