help with this projectile question (1 Viewer)

[ronaldinho]

A boy thrwos a ball from a balcony at a height of 3m above the ground. He throws it with a velocity of 15m/s at an angle of 60degrees to the horizontal.

(a) What is the time to reach the highest point of the ball's motion? done

(b)How long does it take to reach the ground from the highest point?

(c)How far does it travel horizintally?

how do i do the ones in bold? please show working out if possible

 

[airie]

Using the formula (delta)y=u_yt+0.5a_yt²,

Since you know that a_y is simply gravity ie. a_y=-9.8ms^-2, and u_y=u*sin(theta) where u=15m/s and theta=60 degrees, and (delta)y is just -3m as the ground is 3m below the balcony, you get:
-3 = 15 sin(60 degrees)t - 0.5*9.8t².

Then solve for t, and take away the time you got in (a) for the time it takes to reach the ground from the highest point

As for (c), using the formula (delta)x=u_xt+0.5a_xt²,

Since you know that a_x=0 (as there is no force acting on the object horizontally, disregarding air resistance), and u_x=u cos(theta), where u=15m/s and theta=60 degrees, you get:
(delta)x=15 cos(60 degrees)t.

Sub in the time you got in (b) before taking away the time for (a) ie. the solution you get from -3 = 15 sin(60 degrees)t - 0.5*9.8t² for t, you would get (delta)x, which is the range

 

[ronaldinho]

how cna i make t the subject?

 

[SoulSearcher]

I'm assuming you're talking about b), just use the quadratic formula to make t the subject.

 

[ronaldinho]

kk got it.. thanks