A 50kg skier pushes off the top of a hill with an initial speed of 5m/s. Neglect friction. How fast will he be moving after dropping 20m in elevation?
I was wondering if i did this problem correct.
PE + KE_f = KE_i
mgh +1/2mv_f^2 =1/2mv_i^2
50(10)(20) + 1/2 (50)v_f^2 = 1/2(50)(5)^2
10000+ 25v_f^2 =625
25v_f^2=-9375
vf^2=-375
vf=19.36 m/s
No.
Final energy = initial energy
final energy is KE only, so 1/2 mvf^2
initial energy is KE and PE, so 1/2m*5^2 + mg50
1/2 mvf^2= 1/2 m 5^2 + mg50 now solve.
To find the final velocity of the skier after dropping 20m in elevation, you correctly applied the conservation of energy principle. Here's how you can check your calculations:
Starting with the equation:
PE + KE_f = KE_i
Substituting the given values:
50 * 10 * 20 + 1/2 * 50 * v_f^2 = 1/2 * 50 * 5^2
Simplifying:
10000 + 25 * v_f^2 = 625
Rearranging the equation:
25 * v_f^2 = -9375
Dividing by 25:
v_f^2 = -375
Taking the square root:
v_f = √(-375)
At this point, you made an error in the calculation. The square root of a negative number is not a real value. However, in this situation, it indicates that the skier's velocity will be imaginary, representing an impossible scenario. After dropping 20m in elevation, the skier will not have enough potential energy to reach a velocity of 19.36 m/s.
Therefore, based on the given information, you should reconsider your calculations or double-check if there are any other relevant factors or equations that need to be considered in the problem.