A toboggan with two people on it weighs 300 lb. It starts from rest down a...

A toboggan with two people on it weighs 300 lb. It starts from rest down a slope, 1/4 mile long, from a height 200 ft above horizontal level. The coefficient of sliding friction is 3/100 and the force of the wind resistance is proportional to the square of the velocity. When the velocity is 30 ft/sec, this force is 6 lb.

(a) Find the velocity of the toboggan as a function of the distance and of the time.

(b) With what velocity will the toboggan reach the bottom of the slide?

(d) What would its terminal velocity be if the slide were infinite in length?

Answers:

(a) v= 74.1 (e^(0,105t)-1)/(e^(0.105t)+1), v^2=5484(1-e^(-0.0014s)

(b) 68 ft/sec

(d) 74.1 ft/sec

I'm having trouble solving for v originally. Any help would be much appreciated.

Solutions

Expert Solution

I have a strong inclination that there cannot be an exponential function in the velocity function. It is possible only when force due to air resistance is directly proportional to velocity and not its square. I have solved the problem accordingly, Please check !!

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

A 12,000 N car starts from rest and rolls down a hill from a height of...

A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail. (a) Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of 1.2 106 N/m. ? m (b) Calculate the maximum acceleration of the car after contact with the spring,...

An object of mass m1 = 0.435 kg starts from rest at point and slides down an...

An object of mass m1 = 0.435 kg starts from rest at point and slides down an incline surface that makes an angle θ = 36.0° with the horizontal as shown. The coefficient of kinetic friction between the object and the incline surface is 0.395. After sliding down a distance d = 5.60 m, it makes a perfectly inelastic collision with an object of mass m2 = 0.650 kg at point . a) Find the speed of m1 at point just before...

An object of mass m1 = 0.415 kg starts from rest at point and slides down an...

An object of mass m1 = 0.415 kg starts from rest at point and slides down an incline surface that makes an angle θ = 36.0° with the horizontal as shown. The coefficient of kinetic friction between the object and the incline surface is 0.455. After sliding down a distance d = 5.80 m, it makes a perfectly inelastic collision with an object of mass m2 = 0.645 kg at point . (a) Find the speed of m1 at point just before...

A box of mass m1 = 2.0 kg starts from rest and slides down the frictionless...

A box of mass m1 = 2.0 kg starts from rest and slides down the frictionless incline. At point A, the box encounters a (massless) spring of spring constant k. It compresses the spring a distance x = 0.25 m to point B where the speed of the box is 4.4 m/s. The first box is then removed and a second box of mass m2 = 3.0 kg is placed on the same incline at the same initial point and...

A ski starts from rest and slides down a 30 ∘ incline 70 m long. A)If...

A ski starts from rest and slides down a 30 ∘ incline 70 m long. A)If the coefficient of friction is 0.075, what is the ski's speed at the base of the incline? B)If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.

A car start from rest and travels towards a jeep. the jeep starts from rest at...

A car start from rest and travels towards a jeep. the jeep starts from rest at the same time with the car and travels toward the car. the car and jeep is 10 km apart. if the acceleration of the jeep and the car are 4 m/s^2 and 7 m/s^2 repectively, when and where will they meet?

A ski jumper starts from rest from point A at the top of a hill that...

A ski jumper starts from rest from point A at the top of a hill that is a height h1 above point B at the bottom of the hill. The skier and skis have a combined mass of 80 kg. The skier slides down the hill and then up a ramp and is launched into the air at point C that is a height of 10m above the ground. The skier reaches point C traveling at 42m/s. (a) Is the...

The elevator starts from rest at the first floor of the building and comes to a...

The elevator starts from rest at the first floor of the building and comes to a complete stop at the 6th floor. It can accelerate at 6 ft/s2 and then decelerate at 2 ft/s2 Determine the shortest time is takes to reach the 6th floor, which is 60 ft above the ground. Draw the v?t and s?t graphs for the motion of the elevator.

A hoop with a mass of 3.15 kg starts from rest at the top of a...

A hoop with a mass of 3.15 kg starts from rest at the top of a ramp. The ramp is 5.0 m long and 2.1 m high. What is the rotational kinetic energy of the hoop after it has rolled without slipping to the bottom? 16 J 32 J 22 J 78 J

A skier with a mass of 75kg starts from rest at the top of a slope...

A skier with a mass of 75kg starts from rest at the top of a slope which is 110m tall and skis to the bottom. Hint: you must use conservation of energy to solve both parts of this problem. a. What is the skier’s speed at the bottom of the slope if there is no friction? b. If the speed of the skier at the bottom of the slope is actually 20m/s, how much work is done by friction?

Subjects