In order for a ski jumper to attain maximum projectile distance she must reach a velocity of 30m/s. of the runway of the takeoff ramp is 70m long, how quickly ust she accelerate?
To calculate the acceleration required for the ski jumper to reach a velocity of 30 m/s, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (30 m/s in this case)
u = initial velocity (0 m/s, as the ski jumper starts from rest)
a = acceleration (what we're trying to find)
s = displacement (70 m, the length of the runway)
Rearranging the equation to solve for acceleration (a), we get:
a = (v^2 - u^2) / (2s)
Substituting the given values, we have:
a = (30^2 - 0^2) / (2 * 70)
a = 900 / 140
a ≈ 6.43 m/s^2
Therefore, the ski jumper must accelerate at approximately 6.43 m/s^2 in order to reach a velocity of 30 m/s on a runway that is 70 m long.