Help with projectile motion

[rife168]

Would someone be able to briefly clarify these questions for me? I'm a bit rusty after the holiday break..


edit: accidentally cropped the top section, fixed now.

[Aurelian]

Key; # = delta symbol

Q25:
Ek = 1/2mv^2 = 1/2 x 0.20 x 12^2 = 14.4J

Q26:
|#U| = mg|#h| = 0.20kg x 10Nkg-1 x 3.0m = 6.0J

Q27:
Ek total = Ek initial - |#U| = 14.4J - 6.0J = 8.4J

Q28:
Ek = 8.4J
Ek = 1/2mv^2 = 8.4J
mv^2 = 16.8J
m = 0.20kg
Therefore v^2 = 84
v = 9.2ms-1

Q29:
D, Vertically down. The only acceleration at play here is that due to gravity, and this is always towards the Earth.

Hope this helps! Any questions let me know

[rife168]

Q27:
Ek total = Ek initial - |#U| = 14.4J - 6.0J = 8.4J

Would you be able to briefly explain that? Conceptually rather than just in terms of this question. Thanks.

[paulsterio]

This is conservation of energy, any energy gained by an increase in height has to equal the energy lost as kinetic energy. Imagine trying to roll a marble up a slope. As the marble gains height, its Gravitational Potential Energy increases. However, the marble also gets slower and slower as it goes up the slope. This is a loss in kinetic energy.

Thus, E_k(initial) + E_g(initial) = E_k(final) + E_g(final)
In this question, however, E_g(initial) = 0J, E_k(initial) = 14.4J, E_g(final) = 6.0J.


Substitute it in and you will get: 14.4 + 0 = E_k(final) + 6.0


Solve for E_k(final) and you'll get 8.4J - like Aurelian

[rife168]

Thanks, makes sense. I still got 8.4J using vectors and whatnot, but that clears up conservation of energy. Thank you.

[Chenpionn]

apologies for digging up an old thread, but i just want to know whether it would be required to calculate the gravitational potential energy at 1.4m (2.8J) rather than assume that it is 0J at its launch point

[#1procrastinator]

you can take it to be the origin (so yes, 0 potential energy) just make sure you are consistent with your choice of coordinates