Final answer:
To determine if the secret agent will make it across the gorge safely, we analyze the motion of the skier and calculate the time it takes for the skier to reach the other side of the gorge and the horizontal distance covered. The skier falls short and lands in the gorge.
Step-by-step explanation:
To determine if the secret agent will make it across the gorge safely, we need to analyze the motion of the skier. Since the motion is only in the vertical direction, we can use the equations of motion to calculate the time it takes for the skier to reach the other side of the gorge and the horizontal distance covered during this time.
First, let's find the time it takes for the skier to reach the snow patch below. Using the equation y = y0 + v0y * t + (1/2) * a * t^2, where y is the vertical distance, y0 is the initial vertical position, v0y is the initial vertical velocity, a is the acceleration, and t is the time, we can plug in the given values:
y = -100 m (since the snow patch is 100 m below), y0 = 0 m (since the skier starts at the top of the slope), v0y = 60 km/h * sin(30°) = 30 km/h = 8.33 m/s, a = -9.8 m/s^2 (since the skier is moving opposite to the direction of gravity)
By substituting these values into the equation, we can solve for t:
-100 m = 0 + (8.33 m/s)t + (1/2)(-9.8 m/s^2)t^2
After solving this quadratic equation, we get two solutions: t ≈ 0.95 s and t ≈ 11.9 s.
Since the agent is trying to escape, it's safe to assume that he would want to clear the gorge as quickly as possible. Therefore, we take the smaller value of t, which is approximately 0.95 s
Next, let's find the horizontal distance covered during this time. Using the equation x = v0x * t, where x is the horizontal distance, v0x is the initial horizontal velocity, and t is the time, we can plug in the given values:
x = v0x * t = 60 km/h * cos(30°) * 0.95 s = 24.9 m
The skier covers a horizontal distance of approximately 24.9 m during the time it takes to reach the snow patch below. Since the gorge is 60 m wide, which is greater than the horizontal distance covered, the skier does not make it across the gorge safely.
Therefore, the correct answer is b) No, he falls short and lands in the gorge.