Aforce is applied to a box of 10.0 kg for 4.0 s. the box goes from rest to 25 m/s in that time. what is the magnitude of that force?

Final momentum of the box = (mass) x (speed) = (10kg) x (25m/s) = 250 kg-m/s .

Impulse delivered by the force = final momentum of the box = (force) x (time)

250 kg-m/s = (force) x (4 sec)

Divide each side by (4 sec):

Force = (250 kg-m/s) / (4 sec)

Force = (250/4) kg-m/s²

Force = 62.5 Newtons

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.