Question

- For an object being launched at ground level at a tilted non-zero initial velocity, is the velocity zero anywhere? Are the horizontal or vertical components of the velocity zero at any point?

- What is the shape of this trajectory? (Use the mathematical term).

- If an object is launched with a strictly horizontal initial velocity, what is the vertical component of the initial velocity?

- Will an object take longer, less, or the same amount of time to reach the ground if it is dropped from rest rather than launched with a strictly horizontal initial velocity? Try using the simulation to help you determine this. For the free fall simulation, have the cannon point downwards and set the initial velocity to 0 m/s. Use the time, range, height sliding tool to determine the amount of time it took for the cannon to reach the ground. For the horizontal launch, change the angle to 0 degrees and give the cannon an arbitrary non-zero initial velocity. Again use the time, range, and height sliding tool to determine the amount of time it takes for the cannon to reach the ground. Compare these times.

- With a strictly horizontal launch (with an angle of 0 degrees from the horizontal), how does the initial velocity affect the trajectory (specifically the range)? Use the simulation to help you obtain your answer.

Answer #1

Change the Gravity to 9.80 m/s2.. Keep the
height of the cannon at ground level.
Determine what angles you must have the cannon tilted at to
have the cannon ball land at the target 20.5 m away when you have
an initial speed of 20 m/s using the simulation. Let the mass of
the cannon ball remain at 17.60 kg and the diameter at 0.18 m. Then
use the Range formula
R=v02sin(2θ)g
to verify the angles. (Hint: recall from Trigonometry...

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A streamlined and compact projectile is launched from flat
ground on a valley toward a distant hillside at an Army testing
ground in Nevada. The projectile’s initial speed is vi = 150. m/s
as it leaves the cannon. The initial angle of launch θi of the
projectile is unknown. The projectile makes impact high on the
distant hill a time t = 3.00 s after its departure. From GPS
sensors we know that the site of impact is a straight-line...

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ground on a valley toward a distant hillside at an Army testing
ground in Nevada. The projectile’s initial speed is vi = 150. m/s
as it leaves the cannon. The initial angle of launch θi of the
projectile is unknown. The projectile makes impact high on the
distant hill a time t = 3.00 s after its departure. From GPS
sensors we know that the site of impact is a straight-line...

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