For lab we used a projectile launcher which fired a steel ball at a desired angl

Question

For lab we used a projectile launcher which fired a steel ball at a desired angle, and with three different muzzle velocities

a) To find the initial velocity, you can fire the launcher and either measure x and t and use the equation , or you or you can fire the launcher and measure x and y0 and use .Which one is less error-prone experimentally? Why?

b) There are man ways to determine the muzzle velocity; what are two? Be creative but not ridiculous. Given the tools we would likely have at a small college or even a small budget of ~$1k, how would you determine the muzzle velocity?

c) What should happen if you compared a ball launched at 60 degrees and another at 30 degrees? Explain in words the relative sizes of the initial velocities in the x-, and y-directions and the time of flight in these two cases.


Thank you, will vote best answer!!!!

Explanation / Answer

a) using x and y0 would be less error prone Reasoning: in the case of measuring x and t, you are asked to measure a quantity in which precision is very low. Time is dependent on stopping a watch at the very moment it hits the ground which will usually have very low precision in the case of measuring x and y0, y0 is easy to calculate because it requires the use of a ruler or tape measure to calculate the height the projectile launcher is from the ground which will not change from trial to trial b) procedure 1: determine the range of the projectile by using a tape measure to measure the horizontal distance from the muzzle to the point the steel ball lands on a carbon paper. Determine, using a stop watch, the time it takes for the ball to reach from the muzzle to the carbon paper. use the equation: x = (vo*cos(angle))(t) where x is the range where vo is the initial muzzle velocity where angle is the angle at which the muzzle is set where t is the time procedure 2: use a ruler or tape measure to measure the initial height from which the ball is released, y0. Use a stop watch to determine the time it takes for the ball to reach the carbon paper. use: y = (vo*sin(angle))(t) + (1/2)(a)(t^2) where y is the displacement (which will be -y0) where vo is the initial muzzle velocity where angle is the angle to which the muzzle is set where t is the time where a is the acceleration (gravity = -9.8) c) since 30 and 60 degrees are complementary angles (angles that sum to 90), the ball should land at relatively the same location. the initial velocity in the x direction will be larger in the 30 degree case, but will have a much smaller initial y-velocity the initial velocity in the x direction will be smaller in the 60 degree case, but will have a much larger initial y - velocity The 60 degree ball will be in the air longer.

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