Final answer:
To determine the initial speed 'va' and the speed at which the skier strikes the ground 'vb', you can break down their motion into horizontal and vertical components. Use trigonometry to find the initial horizontal and vertical velocities, and then apply the equations of motion to find the time and the speed at which the skier strikes the ground.
Step-by-step explanation:
To determine the initial speed and the speed at which the skier strikes the ground, we need to break down the skier's motion into horizontal and vertical components. Let's call the initial velocity of the skier 'va' and the angle of the ramp 'ua'.
Using trigonometry, we can find the initial horizontal velocity 'vax' by multiplying the initial speed 'va' by the cosine of the angle 'ua':
vax = va * cos(ua)
The initial vertical velocity 'vay' can be found by multiplying the initial speed 'va' by the sine of the angle 'ua':
vay = va * sin(ua)
Since the acceleration due to gravity acts vertically downward, there is no horizontal acceleration. Therefore, the horizontal component of the velocity remains constant:
vbx = vax
For the vertical component, we can use the equation of motion to find the time 't' it takes for the skier to reach the ground:
vby = vay - gt
Solving for 't', we get:
t = (vay - vby) / g
Finally, we can find the speed at which the skier strikes the ground 'vb' by multiplying the horizontal component of the velocity 'vbx' by the cosine of the angle 'ua' and the vertical component of the velocity 'vby' by the sine of the angle 'ua', and taking the square root:
vb = sqrt((vbx^2) + (vby^2))