10/21/13

What is the tension?
A 108 N lamp is hung up with two ropes that each make 20º angles with the horizontal. What's the tension in the ropes? What's the tension if the angle is 60º?
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10/21/13

How fast would a 15 kg box accelerate?
How fast would a 15 kg box accelerate down a 25º snowy slope if the coefficient of kinetic friction were 0.15?
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10/21/13

What is minimum amount?
A sled of mass 40 kg is pulled along flat, snow-covered ground. The static friction coefficient is 0.28, and the kinetic friction coefficient is 0.0800. What is minimum amount of force needed to... more
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10/21/13

Find the acceleration?
A 10 kg box is resting on a smooth (frictionless) horizontal surface of a table. You pull the box by the attached ribbon with a force of 40 N at a 30 degrees angle from the surface of the table.... more
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10/21/13

Find the angle?
Find the angle theta (from its cosine) between v=[1, sqrt(3)] and w=[1, 0].   These are vectors with 1 on top, sqrt(3) on bottom. And 1 on top, 0 on bottom for w. But how do I find the angle?... more
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10/20/13

Compute v and w?
If v+w=[5, 1] and v-w=[1, 5], compute v and w.   This is vectors, 5 on top, 1 on bottom. And 1 on top, 5 on bottom.
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10/17/13

Find the scale reading?
A person with mass of 55 kg is standing on a scale in an elevator. The elevator is moving up and accelerating at 1.5 m/s^2 for 3 seconds, then continues with constant speed. Find the scale reading... more
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10/17/13

What is the force due to gravity?
A 10 kg mass on a horizontal friction-free table is accelerated by a string attached to 12 kg mass hanging vertically from a pulley. a) What's the force due to gravity on the 12 kg hanging mass? b)... more
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10/17/13

Is the rope in danger of breaking?
A 80 kg container is lifted by a rope. The rope is guaranteed not to break if the tension is up to 800 N. The container started at rest, and after 2 seconds is moving at 3.0 m/s. Is the rope in... more
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10/06/13

Use the backward Euler method?
Use the backward Euler method with h=0.025 of y'=(t^2-y^2)sin y, y(0)=-1 at t=0.1, 0.2, 0.3, and 0.4.   Answer: -0.926341, -0.867163, -0.820279, -0.784275
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10/06/13

Use the Euler method?
Use the Euler method with h=0.05 to find approximate values of y'=3+t-y, y(0)=1 at t=0.1, 0.2, 0.3, and 0.4.   Answer: 1.1975, 1.38549, 1.56491, 1.73658
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10/02/13

Find the general solution?
Find the general solution of x'=(2, 1, -5, -2)x+(-cos(t), sin(t)).   (this is 2x2 matrix with 2 and 1 on the left, -5 and -2 on the right. And -cos(t) on top, sin(t) on bottom. I've found the... more
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09/29/13

Find the general solution?
Find the general solution of x'=(-cos t, sin t). ( this is 2×1 matrix with -cos t on top, sin t on bottom.)    Please use the method of undetermined coefficients. 
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09/25/13

Find the general solution?
Find the general solution of x'=(1, sqrt(3), sqrt(3), -1)x+(e^t, sqrt(3)*e^-t). (this is 2x2 matrix with 1 and sqrt(3) on the left, sqrt(3) and -1 on the right. And 2x1 matrix with e^t on top,... more
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09/23/13

What was his initial speed?
A man jumped horizontally from a window and reached the ground 0.80 s later. If he landed 3.6 m from the base of the building, what was his initial speed? How high was the window above the ground?  
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09/23/13

How high is the fort?
A cannon ball leaves a fort with an initial horizontal speed of 1.8*10^2 m/s and strikes a ship in the sea below 7.2 s later. How high is the fort above sea level?
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09/22/13

Find the integral?
∫ [1, 0]ds from 0 to t   (it's matrix with 1 on top, 0 on bottom.)
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09/21/13

Find the general solution?
Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (this is 2x2 matrix with 2 and 3 on left, -1 and -2 on right. And I know how to find the general solution for the 2x2 matrix but not the... more
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09/20/13

Estimate its range?
A projectile was launched from level ground with an initial speed of 340 m/s at 35 degrees to the horizontal. Estimate its range and time of flight.
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09/20/13

Find its time of flight?
A shell was fired from ground level with an initial speed of 350 m/s at an angle of 30 degrees to the horizontal. Assuming there is no air resistance, calculate:   a) its time of flight; b) its... more
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09/20/13

Find the bullet's range?
A bullet was fired horizontally from the top of a 150 m tall tower at 280 m/s. Find the bullet's range and time of flight. Determine also its speed on impact with the ground below.
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09/20/13

What was the range?
A projectile is fired with a horizontal speed of 25 m/s from the top of a mountain of height 110 m. What was the range and time of flight of the projectile?
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09/20/13

Please help me with this physics problem?
A cannon ball leaves a fort with an initial horizontal speed of 180 m/s and strikes a ship in the sea below 7.2 s later. What is the ball's range? How high is the fort above sea level?
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09/19/13

Please help me with this math problem?
Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (2 and 3 on the left, -1 and -2 on the right. e^t on the top, t on the bottom.)    
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09/18/13

Please help me with this math problem?
Let J=(λ, 0, 1, λ), where λ is an arbitrary real number. (2x2 matrix, λ and 0 on the left, 1 and λ on the right.)   (a) Find J^2, J^3, and J^4. (b) Use an inductive argument to show that... more
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