Rate magnitude of vertical component

[hulahoop09]

A skier is moving at 85 km/hr straight down a tall mountain having a slope of 60 degrees. At what rate is the magnitude of the vertical component of his trip decreasing?

I just don't understand exactly how to find it. The wording doesn't make sense to me and I don't know where to start.

 

[tiny-tim]

Welcome to PF!

Hi hulahoop09! Welcome to PF!

A skier is moving at 85 km/hr straight down a tall mountain having a slope of 60 degrees. At what rate is the magnitude of the vertical component of his trip decreasing?
…
The wording doesn't make sense to me …

Yes, it's not the most straightforward way of describing it, is it?

The "vertical component of his trip" is simply his height (measured vertically, relative to something like sea-level).

"Magnitude" just means "size" … and could just as well have been left out completely!

So the question is really, at what rate is his height decreasing?

 

[thomate1]

I can provide an explanation and solution to this problem. The magnitude of the vertical component refers to the strength or intensity of the vertical motion of the skier. In this case, the skier is moving straight down a mountain with a slope of 60 degrees at a speed of 85 km/hr.

To find the rate at which the magnitude of the vertical component is decreasing, we need to consider the forces acting on the skier. The primary force acting on the skier is gravity, which is pulling the skier down the slope. As the skier moves down the mountain, the slope becomes less steep, causing the magnitude of the vertical component to decrease.

To calculate the rate of decrease, we can use the formula for acceleration: a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. In this case, the initial velocity (vi) is 85 km/hr and the final velocity (vf) is decreasing as the skier moves down the mountain. We can also assume that the time (t) is constant.

To find the final velocity, we can use trigonometry to determine the vertical component of the skier's velocity. Since the slope of the mountain is 60 degrees, the vertical component can be found using the sine function: vertical velocity = 85 km/hr * sin(60) = 73.6 km/hr.

Plugging in the values, we get a = (73.6 km/hr - 85 km/hr)/t. As the skier continues to move down the mountain, the final velocity will decrease, resulting in a negative acceleration (deceleration). This means that the magnitude of the vertical component is decreasing at a rate of 11.4 km/hr per unit of time.

In conclusion, the rate at which the magnitude of the vertical component is decreasing for the skier moving at 85 km/hr down a 60 degree slope is 11.4 km/hr per unit of time.