the pilot of a new stealth helicopter which has a mass of 15000 kg and was traveling 180 m / s accelerated to 250 m / s in six s
1 answer:
Answer:
<em>pf = 3750000 kg.m/s</em>
<em>F = 175000 N</em>
Explanation:
<u>Constant Acceleration</u>
An object moves with constant acceleration if its velocity changes uniformly in time.
If we call vo to the initial speed, vf the final speed, and t the time, then the acceleration is calculated as:
The new stealth helicopter was traveling at vo=180m/s and changed to vf=250 m/s in t=6 seconds, thus the acceleration was:
<em>Please note this number is shown rounded to the nearest hundredth, but it was stored in the calculator's memory with full precision. This fact affects the next calculation as will be noted below.</em>
The acceleration must be produced for some net force that can be calculated by:
F = m.a
Where m=15000 Kg is the mass of the helicopter. Thus:
F = 15000 * 11.67
F = 175000 N
<em>The above product would lead to the inaccurate result of 175050 if the acceleration would have not used with its full representation in the calculator's memory.</em>
The momentum of an object of mass m and velocity v is:
p = m. v
The final momentum of the helicopter is:
pf = m.vf = 15000*250 m/s
pf = 3750000 kg.m/s
<u>Note: When performing calculations over intermediate results, it's important to keep them as accurate as possible to preserve the accuracy of the final result.</u>
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Answer:
a) θ=210°, b) t=1.155hr, c) t=1.333hr, d) t=1.333hr, e) θ=180° (straight across), f) t=1hr.
Explanation:
So, the very first thing we nee to do when solving this problem is draw a diagram that represents it. In the attached picture I show a diagram for each part of this problem.
part a)
So, for her to move in a direction directly opposite her starting point, the x-component of her velocity must be de same as the velocity of the river in the opposite direction. We can use this fact to find the angle we need. If we analize the triangle I drew in the diagram, we can ses that:
When solving for theta, we get that:
so now we can substitute the corresponding values:
Which yields:
but we are measuring the angle relative to the line perpendicular to the river, positive if down the river. So we need to subtract the angle from 270° so we get:
θ=270°-60°=210°
part b)
for part b, we need to find what the y-component for the velocity of the boat is for an angle of 210° as shown in the problem, so we get that:
The woman will head in a negative 5.60km distance from one side to the other, so we get that the time it takes her to go to the other side of the river is:
part c)
In order to find the time it takes her to travel 2.80km down and up the river, we need to find the velocities she will have in both directions. First, down stream:
and now up stream:
Once we got these two velocities we will now need to find the time to take each trip:
time down stream:
and the time up stream:
so the total time will be:
d) the time it takes the boat to go upstream and then downstream for the same distance is the same as the time we got on part c, since both times will be the same but they will come in different order, but their sum will be just the same:
t=1.333hr
e) For her to cross the river faster, she must row in a 180° direction (this is in a direction straight accross the river) that way she will use all her velocity to move across the river. (Even though she will move a certain distance horizontally and will not reach a point opposite to the starting point.)
f) In order to find the time it takes her to get to the other side, we need to divide the distance into the velocity of the boat.
so
t= 1hr
