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Consider an airplane that normally has an airspeed of 120 km/h in a 75 km/h crosswind blowing from west to east. Calculate its ground speed when its nose is pointed north in the crosswind.

____ km/h

Mar 3rd, 2015

Ok, we'll assume that the crosswind completely pushes the plane 75 km/h off course.

To find the answer, we need to do vector addition.

We need to calculate the resultant vector found by adding the normal speed with the speed of the crosswind.

Notice that the three vectors form a right triangle, with the resultant vector acting as the hypotenuse . We'll make use of the Pythagorean Theorem to solve for the magnitude of the resultant speed...

c^2 = a^2 + b^2

c = SQRT ( 120^2 + 75^2)

   = SQRT (14400 + 5625)

   = SQRT (20025)

 = 141.51 km/hr

Mar 3rd, 2015

where do the .5 come from?

Mar 3rd, 2015

I assume you mean in the answer 141.5 ?

Its a question of where we should round the answer. In my calculator I get the actual answer, after taking the square root of 20025...


which I rounded to  141.5

Mar 3rd, 2015

Forces of 5.0 N and 8.0 N act at right angles on a block of mass 3.0 kg. How much acceleration occurs?

Mar 3rd, 2015

Same idea as the plane, we use vector addition.

The resultant force vector is 9.4 N, found by the use of the Pythagorean Theorem...

= SQRT (8^2 + 5^2)

=9.43398 N

But we want the acceleration, not just the force, so we use Newton's First Law...

F = m*a

...and solve for a...

a = F/m

a = 9.43398 N / 3.0 kg

   = 3.14 m/s/s

Mar 3rd, 2015

A firefighter of mass 98 kg slides down a vertical pole with an acceleration of 4.9 m/s2. What is the friction force that acts on the firefighter?

_____ N

Mar 3rd, 2015

We can assert that we know what the firefighter's acceleration would be if friction were not present.  He would fall at 9.8 m/s^2 (as would any object in free-fall).  But, due to the friction on the pole, he accelerates only at 4.9 m/s^2--half of the maximum value.  The force of friction essentially de-accelerates the firefighter by 4.9 m/s^2, found by the calculation...

9.8m/s^2 - 4.9m/s^2 = 4.9m/s^2  

The force of friction is found by taking this accleration and multiplying it by the mass of the firefighter...

F = ma

F = 98 kg * 4.9 m/s^2

 = 480.2 N  

Mar 3rd, 2015

A ball is thrown with enough speed straight up so that it is in the air several seconds. What is its velocity .50 s before it reaches its highest point?

_______ m/s

Mar 3rd, 2015

The acceleration of the ball will be 9.8m/s^2 (as it would be for any object). Because as the ball goes up and up until it reaches its highest point, it will be slowing down, then we'll write the acceleration as a negative number...

a = -9.8 m/s^2

Recall that acceleration is defined as the change in velocity over a given time interval. We know from experience that a ball thrown straight up into the air, when it reaches its highest point, that it will momentarily stop before it changes direction and begins to fall. Since the ball comes to rest at the highest point we'll call this velocity, velocity 2 (v2), and assign it a value of 0 m/s.

We want to know the velocity 0.50 s before the highest point. We'll call this velocity, velocity 1 (v1), since it occurs before velocity 2 (v2). 

So, taking acceleration to be given by the equation...

a = (v2 - v1) / t

..where t is the time interval...

we can rearrange to solve for v1...

- v1 = (a * t) - v2

...multiplying both sides by -1 yields...

v1 = - (a * t) + v2

Now substitute the values   a = -9.8m/s^2    t = 0.50 s    v2 = 0 m/s

v1 = - (-9.8 * 0.50) + 0

= 4.9 m/s


Mar 3rd, 2015

Last one I need help with

A canoe is paddled at 2.0 km/h directly across a river that flows at 3.0 km/h, as shown in the figure. What is the resultant speed of the canoe relative to the shore?

______ km/h

Mar 3rd, 2015

Another vector addition...

The resultant vector is found by use of the Pythagorean Theorem...

= SQRT (2^2 + 3^2)

= SQRT (4 + 9)

= SQRT (13)

= 3.60555

= 3.61 km/h

Mar 3rd, 2015

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