Projectiles Help! Last Question! Thanks =)?

Question

A stone is thrown at 45degrees to the horizontal. It reaches its peak height after 1.50 seconds.

find (a) the vertical component of its initial velocity
- I done this and got 20.81m/s?

(b) the horizontal component of its initial velocity
- Would I be right in thinking this is the same as the vertical component (20.81m/s) as it is at an angle of 45degrees?

(c) the horizontal distance from the point where it was thrown to the point where it hits the ground.
- 62.43m? I assumed that my previous answer was right.

Also:
A rope is pulled with a 600N force attached to a boulder. The rope makes a 30degrees angle with the direction in which the boulder is travelling. Find the force which is pulling the boulder forwards and the force with pulls it sideways.

-Would this just involve finding the vertical and horizontal components? So 300N and 519.6N respectively?

Thanks a lot for your time =)

Answer 1

> find (a) the vertical component of its initial velocity
> - I done this and got 20.81m/s?

No--not sure how you got that. Gravity is 9.8m/s², which means that the stone loses 9.8m/s² of vertical speed every second while it's rising. So after 1.5 seconds, it would have lost (9.8m/s²)×(1.5s) = 14.7 m/s. (not 20.81 m/s).

> (b) the horizontal component of its initial velocity
- Would I be right in thinking this is the same as the vertical component...

Yes.

> ... (20.81m/s) ...

Right idea, wrong number (see (a))

> (c) the horizontal distance...
> - 62.43m?

Right idea, wrong number.

> A rope is pulled with a 600N force attached to a boulder....

This is a poorly worded question, because they don't tell you if the boulder is traveling horizontally, vertically or some mix; and they don't tell you whether the 30 degrees is up or to the side or what. Then they throw in the terms "forward" and "sideways" with no reference.

I _think_ there is no vertical component here. I think they're saying that boulder's moving (say) north, and the rope is pulling (horizontally) at an angle 30 degrees "west of north." In this case, the "forwards" force would be the "north" component and the "sideways" force would be the "west" component. That's the best sense I can make of it.

Answer 2

(a) The solving formula should be
vy0 - gt = 0 vy0 = gt
where g = 9.8 m/s2 and t = 1.5 s

(b) That's correct

(c) The stone hits the ground when its position in y axis is 0
The position in y axis is given by the formula
y(t) = vy0*t - 1/2*g*t^2
by putting y=0 eqiation can be solved on t ( discarding the solution t=0)
Once the value t has been determined it can be used in the formula that gives the position on x axis
x(t) = vx0*t

Thte problem of the rope consists of decomposing the vector with modulo 600N along x and y axis.that is by equations
x = 600N * cos 30
y = 600N * sin 30