You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30 0 above horizontal, the ball hits the bull’s-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit the bull’s-eye in its new position? (Mathematically there are two solutions to this problem: the physically reasonable answer is the smaller of the two.)
You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30 0 above horizontal, the ball hits the bull’s-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit the bull’s-eye in its new position? (Mathematically there are two solutions to this problem: the physically reasonable answer is the smaller of the two.)
You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 300above horizontal, the ball hits the bull’s-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit the bull’s-eye in its new position? (Mathematically there are two solutions to this problem: the physically reasonable answer is the smaller of the two.)
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
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