You push a skateboard so that it rolls down the road at a speed of 1.00 m/s. You run after the skateboard and jump off the ground with speed 3.80 m/s and an angle of 29.0° above the horizontal hoping to land on the skateboard. How much distance do you need between you and the skateboard to land on it?
Question
You push a skateboard so that it rolls down the road at a speed of 1.00 m/s. You run after the skateboard and jump off the ground with speed 3.80 m/s and an angle of 29.0° above the horizontal hoping to land on the skateboard. How much distance do you need between you and the skateboard to land on it?
Solution
To solve this problem, we need to find the horizontal distance covered by the person while in the air. This can be found using the equations of motion.
Step 1: Find the horizontal and vertical components of the initial velocity of the person.
The horizontal component (Vx) is given by V*cos(θ) = 3.80 m/s * cos(29.0°) = 3.30 m/s.
The vertical component (Vy) is given by V*sin(θ) = 3.80 m/s * sin(29.0°) = 1.83 m/s.
Step 2: Find the time the person is in the air.
This can be found using the equation of motion: Vy = g*t, where g is the acceleration due to gravity (9.81 m/s²). Solving for t gives t = Vy / g = 1.83 m/s / 9.81 m/s² = 0.187 s.
Step 3: Find the horizontal distance covered by the person.
This is given by the equation d = Vx * t = 3.30 m/s * 0.187 s = 0.617 m.
Step 4: Find the distance between the person and the skateboard when the person jumps.
This is given by the difference in the distances covered by the person and the skateboard, which is d = 0.617 m - (1.00 m/s * 0.187 s) = 0.617 m - 0.187 m = 0.430 m.
So, you need to be 0.430 m away from the skateboard when you jump to land on it.
Similar Questions
Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19degrees ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest hundredth of an inch if necessary.
Sitting on a park bench, you see a swing that is 100 feet away and a slide that is 80 feet away. The angle between them is 30°. What is the approximate distance between the swing and the slide?A.149 feetB.161 feetC.50 feetD.24 feet
Allison is skateboarding across a level road. The coefficient of static friction is 0.450 between Allison's shoes and the skateboard. If there is a hole in the road 13.1 m up ahead and Allison is able to stop without sliding off of the skateboard, what is the maximum velocity she could have initially been travelling?
A professional skier reaches a speed of 39.6 m/s on a 30° ski slope. Ignoring friction, what was the minimum distance along the slope the skier would have had to travel, starting from rest?Select one:a.640 mb.160 mc.320 md.110 m
A body is projected downward at an angle of 30° to the horizontal with a velocity of 9.8 m/s from the top of a tower 29.4 m high. How long will it take before striking the ground?A 2 s B 5 s C 8 s D 10 s
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.