James Bond is trying to jump from a bridge and land on the first car of a moving train that is going to pass under the bridge. The train moves at 85 km/h and the vertical height between the bridge and the top of the carriage is 15 m. if Bond gets a running start of 4.2 m/s horizontally as he leaps off the bridge, where would the train be ( relative to the bridge ) when he jumps off?
(
which way horizontally is he running? Wouldn't that matter?
I would assume in the same direction as the train
To answer this question, we need to calculate the time it takes for James Bond to reach the train after jumping off the bridge. We can use the kinematic equation for vertical motion:
Δy = v0y * t + (1/2) * a * t^2
Where:
Δy = vertical displacement (height of the carriage) = 15 m
v0y = initial vertical velocity = 0 m/s (as Bond jumps horizontally)
a = acceleration due to gravity = 9.8 m/s^2
t = time
Since Bond jumps off horizontally, his initial vertical velocity is zero. Therefore, the equation simplifies to:
Δy = (1/2) * a * t^2
Now, let's solve for t:
15 m = (1/2) * 9.8 m/s^2 * t^2
Dividing both sides by (1/2) * 9.8 m/s^2, we get:
t^2 = 15 m / ((1/2) * 9.8 m/s^2)
t^2 = 3.06 s^2
Taking the square root of both sides, we find:
t ≈ 1.75 s
Therefore, it takes approximately 1.75 seconds for Bond to reach the train after jumping off the bridge. We can calculate how far the train travels during this time using the equation:
distance = speed * time
Given that the train is moving at a speed of 85 km/h, we need to convert this to m/s:
85 km/h = 85,000 m / 3600 s ≈ 23.61 m/s
distance = 23.61 m/s * 1.75 s
distance ≈ 41.34 m
Therefore, the train will be approximately 41.34 meters away from the bridge when James Bond jumps off.