A ball A is thrown vertically upward from the top of a 30-m-high building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.

Two particles A and B start from rest at the origin s = 0 and move along a straight line such that aA = (6t - 3) ft/s^2 and aB = (12t^2 - 8) ft/s^2, where t is in seconds. Determine the distance between them when t = 4 s and the total distance each has traveled in t = 4 s.

A ball is thrown upward with an initial velocity of $30\, \mathrm{\dfrac{m}{s}}$. What is the maximum height that the ball will reach?

A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, another ball is dropped from a building 15 m high. After how long will the balls be at the same height?

A ball is thrown upward with an initial speed of 10 m/s from the top of a building. A second ball is thrown upward with an initial speed of 20 m/s from the ground. Both balls achieve the same maximum height above the ground. How tall is the building?

A stone is thrown from the top of a building with an initial velocity of 20 m/s downward. The top of the building is 60 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground?

If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation a = 9.81[1 - v^2 (10^-4)] m/s^2, where v is in m/s and the positive direction is downward. If the body is released from rest at a very high altitude, determine (a) the velocity when t = 5 s, and (b) the body’s terminal or maximum attainable velocity (as t → ∞).

The acceleration of a rocket traveling upward is given by a = (6 + 0.02s) m/s^2, where s is in meters. Determine the time needed for the rocket to reach an altitude of s = 100 m. Initially, v = 0 and s = 0 when t = 0.

An air-filled rubber ball has a diameter of 6 in. If the air pressure within the ball is increased until the diameter becomes 7 in., determine the average normal strain in the rubber.

When a ball is thrown vertically upward from ground level it raised to a maximum height of 50m. With what speed must a ball be thrown vertically from ground level to rise to a maximum height of 50 m?

A ball is thrown vertically upward from ground level with an initial velocity of 96 feet per second. Use a(t) = -32 feet per second per second as the acceleration due to gravity. (Neglect air resistance.) (a) How long will it take the ball to rise to its maximum height? What is the maximum height? (b) After how many seconds is the velocity of the ball one-half the initial velocity? (c) What is the height of the ball when its velocity is one-half the initial velocity?

A race car travels with a constant tangential speed of 75.0 m/s around a circular track of radius 625 m. Find (a) the magnitude of the car's total acceleration and (b) the direction of its total acceleration relative to the radial direction.

A ball is thrown vertically upward from a height of 6 ft with an initial velocity of 80 ft/s. The signed distance s (in feet) of the ball from the ground after t seconds is given by the position function $s=s(t)=6+80 t-16 t^{2}$. (a) What is the velocity of the ball after 2 s? (b) When will the ball reach its maximum height? (c) What is the maximum height the ball reaches? (d) What is the acceleration of the ball at any time t? (e) How long is the ball in the air? (f) What is the velocity of the ball upon impact with the ground? What is its speed? (g) What is the total distance traveled by the ball?

Solve the given equation.

$$\cos \theta = - 1$$