2 minute read
Range of a Projectile
by AudioLearn
the initial Y will be zero. This means that zero velocity at the apex equals the initial velocity squared minus 2 times the force of gravity times the height Y.
When you shoot the fireworks at 70 meters per second, only a portion of this velocity is in the y direction. How much? Remember that the velocity in the y direction will be the total velocity multiplied by the sin of theta (which is 75 degrees). This leads to an initial velocity in the y direction of 67.6 meters per second. Taking this value, squaring it and dividing by 2 and by 9.8 meters per second squared (the force of gravity) will lead you to the height, which is 233 meters high.
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You can also calculate the time it takes to do this. The equation is the height y equals the initial y plus 0.5 multiplied by the time and multiplied by the sum of the initial velocity in the y direction and the velocity at the peak (which is zero). This becomes 233 equals 0.5 times 67.6 times the time. Using a calculator, you get the time equals 6.9 seconds.
Now that you know the time spent, the angle, and the initial velocity, you can determine how far in the horizontal direction the projectile will be at its apex. The velocity in the horizontal direction will be 70 meters per second multiplied by the cosine of 75 degrees. This will be 18.1 meters per second. The apex happens at 6.9 seconds so the distance in the x direction will be velocity multiplied by the time or will be 125 meters.
RANGE OF A PROJECTILE
How does the initial velocity of a projectile affect the range of the velocity? The greater the initial velocity, the greater will be the range. The initial angle will have a big effect on the range. For a fixed initial speed (as in by a cannon), the maximum range happens at an angle of 46 degrees if no air resistance is involved. If air resistance is considered, the angle will be 38 degrees. The range is also affected by the value of the acceleration of gravity. In other words, you can drive a golf ball further on the moon than you can on Earth.
What you should know is that the range has two angles that will give the same value. The sum of these two angles is going to be 90 degrees. This means that you’ll get the same range if you shoot the projectile at 75 degrees as you would at 15 degrees.
