A student rides on a train traveling at Vt = 36ikm/hr (with the respect to the ground). What are the speed and the velocity of the student with respect to the ground if he runs at 5.0im/s? -5.0 m/s? 5.0j m/s perpendicular to the direction of motion of the train?
Let's convert km/hr to m/s
36km/hr * 1000m/km * hr/3600s = 10m/s
how convenient.
at 5.0i the velocities just add: 10i + 5i = 15im/s
same for -5i: 10i-5i=5im/s
when running at 5.0j, we have 10i+5j, so the speed is sqrt(100+25) = 11.2m/s
direction θ has tanθ = 5/10, so θ=26.6°
36km/hr? what is this, a freight train?
Thank you very much! I appreciate your help! :)
To find the speed and velocity of the student with respect to the ground, we need to consider the relative motion between the student and the train.
1. The student runs at 5.0 m/s in the i-direction (same as the train's direction of motion).
To find the speed of the student with respect to the ground, we can simply add the speed of the student relative to the train (5.0 m/s) to the speed of the train (36 km/hr).
First, let's convert the speed of the train from km/hr to m/s:
Speed of the train = 36 km/hr = (36 × 1000) m/(1 × 3600) s = 10 m/s.
Now, we can calculate the speed of the student with respect to the ground:
Speed of the student = Speed of the student relative to the train + Speed of the train
= 5.0 m/s + 10 m/s
= 15 m/s.
So, the speed of the student with respect to the ground is 15 m/s in the i-direction.
2. The student runs at -5.0 m/s in the i-direction (opposite to the direction of motion of the train).
Similarly, to find the speed of the student with respect to the ground, we need to subtract the speed of the student relative to the train (-5.0 m/s) from the speed of the train (10 m/s).
Speed of the student = Speed of the student relative to the train - Speed of the train
= -5.0 m/s - 10 m/s
= -15 m/s.
Therefore, the speed of the student with respect to the ground is 15 m/s in the negative i-direction.
3. The student runs at 5.0 m/s in the j-direction perpendicular to the train's direction of motion.
Here, we can see that the student's velocity in the j-direction remains the same since the train's motion is only in the i-direction.
So, the velocity of the student with respect to the ground will be 5.0 m/s in the j-direction.
To summarize:
- If the student runs at 5.0 m/s in the i-direction, the speed of the student with respect to the ground is 15 m/s in the i-direction.
- If the student runs at -5.0 m/s in the i-direction, the speed of the student with respect to the ground is 15 m/s in the negative i-direction.
- If the student runs at 5.0 m/s in the j-direction, the velocity of the student with respect to the ground is 5.0 m/s in the j-direction.