Which object has the larger maximum height?
Object A is launched as projectile with initial speed v at an angle θ above the horizontal. Object B has exactly the same initial speed at exactly the same angle as object A but object B is sliding up a frictionless Object A has mass M and object B has mass 2M. During the subsequent motion, each object will...
-------------------------------------------------------

answers:
sojsail say: i. When A is at its maximum height, its velocity in the vertical axis is zero. But the original velocity in the horizontal direction has not changed, so there is kinetic energy from that.
When B is at its maximum height, its velocity in the vertical axis is zero. Its velocity in the horizontal axis is also zero because it is following that frictionless ... whatever. Therefore B is totally motionless and has no kinetic energy.
Therefore object A has the larger kinetic energy at the maximum height.

ii. Solution by the equations of motion:
Object A's vertical component of V is V*sinθ. It is accelerating downward at -g = -9.8 m/s^2. The height it reaches is given by V^2 = U^2 + 2*a*s
0^2 = (V*sinθ)^2 + 2*(-g)*s
s = (V*sinθ)^2 / (2*g)

Object B's analysis will be more convenient with the incline of the incline(?) being the reference. In that case we need to use the downslope component of g: -g*sinθ for the acceleration a.
To find the height it reaches, I will again use V^2 = U^2 + 2*a*s
0^2 = V^2 + 2*(-g)*sinθ*s
s = V^2 / (2*g*sinθ)
Since sinθ is always less than or equal to 1, V^2 / (2*g*sinθ) > (V*sinθ)^2 / (2*g) Therefore B gets higher.
-
RealPro say: sliding up a frictionless.... incline at angle θ above the horizontal???????

When object A reaches max height, it will have 0 velocity in the vertical direction, but some velocity v*cosθ in the horizontal direction.
So only part of its starting kinetic energy will be converted into potential energy, while the rest will be contained in the kinetic energy due to the horizontal motion.

On the other hand, object B will have exactly 0 velocity at max height, if it is launched straight up an incline.
If the incline is frictionless, then ALL of its initial kinetic energy gets converted to potential, and it must reach a larger height
(Max height does not depend on mass for projectiles or for motion on an incline, because m will cancel, so the)
-
Andrew Smith say: Object B is on the ramp. When the vertical component of the velocity is zero ( maximum height ) the horizontal component of the velocity must also be zero.
So ALL the kinetic energy has gone into potential energy.

Object A still has a horizontal component of the velocity at the maximum height so less energy has gone into potential and it will not reach as great a height.
-
vbdiz say: hytifvvs
-
mnwpi say: sibcdkac
-