At time t = 0 a small ball is projected from point A with a velocity of 200 ft/sec at the $60^{\circ}$ angle. Neglect atmospheric resistance and determine the two times $t_1$ and $t_2$ when the velocity of the ball makes an angle of $45^{\circ}$ with the horizontal x-axis.

Repeat earlier problem, only now the driver of car A sees and reacts very unwisely to the police car P. Car A is traveling at $v_{A}$ = 130 km/h as it passes P, but over the next 5 seconds, the car uniformly accelerates to 150 km/h, after which that speed is maintained. If the motion of the police car P remains as described in earlier problem, determine the distance required for the police officer to overtake car A.

Determine the speed v at which the race car will have no tendency to slip sideways on the banked track, that is, the speed at which there is no reliance on friction. In addition, determine the minimum and maximum speeds, using the coefficient of static friction $\mu_{s}=0.90$. State any assumptions. $\rho=1200^{\prime}$

The aircraft carrier is moving at a constant speed and launches a jet plane with a mass of 3 Mg in a distance of 75 m along the deck by means of a steam-driven catapult. If the plane leaves the deck with a velocity of 240 km/h relative to the carrier and if the jet thrust is constant at 22 kN during takeoff, compute the constant force P exerted by the catapult on the airplane during the 75-m travel of the launch carriage.

A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y^2 = [120(10^3)x] m. If the x component of acceleration is ax= a1 4 t2b m>s2,

A small projectile is launched from ground level with an initial speed of 98 m/s. Find the possible angles of elevation so that its range is 490 m.