EK Physics 1001: Question 112

[swiftaspirations]

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

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[swiftaspirations]

Question answered: (KE + PE)i=(KE + PE)f
If you want to use kinetic energy to solve for the max height for a projectile with an initial velocity at an angle, you cannot put zero for the final KE since there is still horizontal velocity at the top of the parabola. Therefore, it is easier to use kinematics equations for this particular problem.

 

[Cawolf]

These questions are really only approachable by thinking about the animal as a simple projectile.

Therefore, the horizontal velocity only alters the range of the jump, not the height.

You are given the vertical velocity, so to say it is the upwards component of a non-existent launch angle is not appropriate.

You always use the vertical component for height. In the ball problem you are given the total velocity (hypotenuse if you will) and you use the sine of the launch angle to determine what component is upwards. In this problem you are already given the upwards velocity - it is 5 m/s at 90 degrees.

 

[amy_k]

Is the TPR example with the ball throwing giving 12m/s as the vertical velocity or the velocity at 85 degrees?

We would have to use the vertical component for velocity to determine the maximum height. The only thing I can think of is that they are determining the initial kinetic energy of the ball as it leaves the hand at 12m/s. Kinetic energy is a scalar, but the 'v' in the 1/2 mv^2 for kinetic energy is v(85 degrees) not vy. We would still have to get to vy at some point, I would have to see where they went with their calculation from there.