Press Fire to launch an object. You can choose the object by clicking on one of

Question

Press Fire to launch an object. You can choose the object by clicking on one of the objects in the scroll-down menu at top right (a is not among the choices) To adjust the cannon angle, click and drag on it or type in a numerical value (in degrees). You can also adjust the speed mas, and diameter of the object by typing in values. Clicking Air Resistance displays settings for (1) the drag coefficient and (2) the (which controls the air density). For this tutorial, we will use an altitude of zero (sea level) and let the drag coefficient be automatically set when the object is chosen. Play around with the simulation. When you are done, click Erase and select a baseball prior to beginning Part A. Leave Air Resistance unchecked. First, you will investigate purely vertical motion. The kinematics equation for vertical (ignoring air resistance) is given by when = 0 is the initial position (which is 12 m above the ground due to the wheels of the cannon.), upsilon_0 is the initial speed, and g is the acceleration due to gravity Shoot the baseball straight upward (at an angle of 90 degree) with an initial speed of 20 m/s How long does it take for the baseball to hit the ground? Express your answer with the appropriate units.

Explanation / Answer

Initial velocity, u = 20 m/s
When the cannon reaches its maximum height, its velocity is zero, v = 0
Using the equation, v = u - gt1,
t1 = u/g
= 20/9.8
= 2.04 s
Using the equation v2 - u2 = 2gH,
H = [u2/2g]
= 400/19.6
= 20.41 m.

Total height from the ground, S = 20.41 + 1.2 = 21.61 m
Using the equation, S = vt + 1/2g(t2)2,
(t2)2 = 2S/g                 [since v = 0]
Time taken to reach the ground, t2 = SQRT[2S/g]
= SQRT[2 x 21.61 / 9.8]
= 2.1 s

Total time = t1 + t2
= 4.14 s

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