You push a skateboard so that it rolls down the road at a speed of 1.40 m/s. You run after the skateboard at a speed of 3.80 m/s and while still behind the skateboard you jump off the ground at an angle of 30.0° above the horizontal hoping to land on the skateboard. How much distance do you need between you and the skateboard to jump and land on it?
sorry it says that its the wrong answer
d1 = V*(Tr+Tf) = 1.4 * 0.388 = 0.543 m. = Distance covered by skateboard while skater is in air.
d2 = Xo*(Tr+Tf) = 3.29 * 0.388 = 1.28 m. = Distance jumped by skater.
d2-d1 = 1.28 - 0.543 = 0.734 m. Between skater and skateboard.
ok thanks got it
To calculate the distance between you and the skateboard when you jump, you can use the laws of projectile motion. Let's break down the problem into components:
1. Vertical component:
- The initial vertical velocity is zero because you jump off the ground.
- The acceleration due to gravity is -9.8 m/s² (negative because it acts downward).
- The angle of 30.0° above the horizontal suggests that the launch angle is 60.0° below the vertical.
2. Horizontal component:
- The initial horizontal velocity is the speed at which you are running, which is 3.80 m/s.
Using these components, we can calculate the time it takes for you to be in the air and reach the same height as the skateboard. Once we have the time, we can calculate the horizontal distance traveled by the skateboard during that time.
Let's find the time first:
1. Use the vertical motion equation:
- final vertical velocity (vf) = initial vertical velocity (vi) + (acceleration due to gravity * time)
Since vf = 0 (at highest point of jump), we can rearrange the equation as:
0 = 0 + (-9.8 m/s²) * time
-9.8 * time = 0
time = 0
2. Use the horizontal motion equation:
- horizontal distance (d) = horizontal velocity (vh) * time
(Since time is 0, the horizontal distance is also 0.)
Therefore, when you jump, you should be directly above the skateboard to land on it. There is no distance needed between you and the skateboard to make the jump successfully.
Vo =3.80 m/s[30o].
Xo = 3.8*Cos30 = 3.29 m/s.
Yo = 3.8*sin30 = 1.9 m/s.
Y = Yo + g*Tr.
0 = 1.9 - 9.8Tr, Tr = =.194 s. = Rise time.
Tf = Tr = 0.194 s. = Fall time.
d = V*(Tr+Tf) = 1.4 * 0.388 = 0.543 m.