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by Anonymous on June 30th, 2008

Anonymous

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Help answer this question below.

A cannonball is fired at a speed of 50 m/s and an angle of 30 degrees. A cannonball that was accidentally dropped hits the moat below in 1.5 seconds. How far from the castle wall does the cannonball hit the ground?

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Answers. 1 helpful answer below.

  • by Tinkerbell on July 1st, 2008

    Tinkerbell

    Here is how to do it rather than actually doing it for you:

    Fristly calculate how high the initial elevation is using the second piece of data given. If you know how long an object, from rest, takes to fall from an elevation and the acceleration, which you do it is acceleration due to gravity so -9.8 m/s^2, you can work out the intial elevation. You should have, or know the equations of motion needed if not google "equations of motion" to get them. You don't really need this information but it will help in undestanding the physics a bit more to work out as much as you can from the initial data.

    Now work out the initial horizontal and vertical components of the velocity of the fired cannonball. You can do this with basic trigonometry. you know the angle and hypotenuese so work out the horizontal and vertical components.

    Next realise this projectile, in the absence of air resistance, will follow a parobolic curve. Imagine it is fired directly up with vertical component of the velocity and work out how long it would take to reach it's initial elevation (i.e. go up and then down again). Again this can be done with the equations of motion. This is the time it will take to reach the initial elevation. SInce you know the horizontal component as well you can calculate how far it will travel horizontally in this time.

    Now the last part is to work out how far it will travel in the time taken to fall the distance bvetween the initial elevation and the ground (which is already given). SO work out how far the ball will travel horizontally in this time.

    now combine the first horizontal distance with the second. That's the total distance.

    It would help greatly to draw a picture of the motion and divide it up as I have detailed so you can visualise it. That's what I used to do.

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