Posted by cyrus on Saturday, November 8, 2008 at 10:50pm.
a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. there is a force due to air resistance of |v|/30, where velocity v is measured in m/sec.
a. find the maximum height above the ground the ball reaches.
b. find the time the ball hits the ground.
you cannot use the kinematic equations.
math/physics - drwls, Saturday, November 8, 2008 at 11:12pm
This IS a kinematics problem. Any equation used to solve it involves kinematics. An exact solution would require solving a (kinematic) differential equation.
A good approximation to part (a) can be obtained by assuming an average air resistance force of |V|/60 , where V is the initial velocity of 20 m/s. Thus work done against friction going up is
V/60*H, and initial kientic energy equals potential energy gain at the highest elevation PLUS work done against friction.
(1/2) M V^2 = M g H + V/60*H
H = (1/2)V^2/[g + V/(60M)]= (1/2)V^2/11
= 18.2 m
The time spent by the ball going up is
very nearly H/(V/2) = 0.46 s
Use a similar energy conservation argument to estimate the (longer) time it takes for the ball to come back down. Note that it must travel an additional 30 m to reach the ground.
math/physics - drwls, Saturday, November 8, 2008 at 11:32pm
M dv/dt = -M g -v/60*H
M dv/dt = -M g + v/60*H
Once you have v(t), integrate v dt to get the distance travelled vs t.
Answer This Question
More Related Questions
- calc - a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec ...
- math-urgent - A ball with a mass 0.15kg is thrown upward with an initial ...
- math - A ball is thrown from the edge of a cliff with an initial velocity of 60·...
- Physics - A ball is thrown from the top of a building with an initial velocity ...
- physics - A ball is thrown from the top of a building with an initial velocity ...
- physics - A ball is projected upward at time t = 0 s, from a point on a flat ...
- Math - If a ball is thrown vertically upward from the roof of 48 foot building ...
- Math Calc - If a ball is thrown vertically upward from the roof of 48 foot ...
- College algebra - When a ball is thrown up into the air, it makes the shape of a...
- Calculus Help - If a ball is thrown vertically upward from the roof of 64 foot ...