E2.4 A laser printer uses a laser beam to print copy rapidly for a computer. The laser is positioned by a control input r(t), so that we have Y(s) = 4(s + 50) R(s) s 2 + 40s + 300 The input r(t) represents the desired position of the laser beam. (a) If r(t) is a unit step input, find the output y(t). (b) What is the final value of y(t)?

Aball is thrown from the top of a building with an initial velocity of 21.9 m/s straight upward, at an initial height of 51.6 m above the ground. the ball just misses the edge of the roof on its way down, as shown in the figure. (a) determine the time needed for the ball to reach its maximum height. (b) determine the maximum height. (c) determine the time needed for the ball to return to the height from which it was thrown, and the velocity of the ball at that instant. (d) determine the time needed for the ball to reach the ground. (e) determine the velocity and position of the ball at t = 5.35 s.

Avector a⃗ has a length of 8.6 m and points in the negative x direction. find the x component of the vector −3.7a⃗ .

Ineed to answer this problem but i lack in knowledge, what should i study to answer this problem? i have never used derivatives in a physics problem so i'm not sure what's happening and i can't find videos explaining.