Answer:
3) D: 31 m/s
4) D: 84.84 metres
Explanation:
3) Initial velocity along the x-axis is;
v_x = v_o•cos θ
Initial velocity along the y-axis is;
v_y = v_o•sin θ
Plugging in the relevant values, we have;
v_x = 31 cos 60
v_x = 31 × 0.5
v_x = 15.5 m/s
Similarly,
v_y = 31 sin 60
v_y = 31 × 0.8660
v_y = 26.85 m/s
Thus, magnitude of the initial velocity is;
v = √(15.5² + 26.85²)
v ≈ 31 m/s
4) Formula for horizontal range is;
R = (v² sin 2θ)/g
R = (31² × sin (2 × 60))/9.81
R = 84.84 m
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Answer:
Surely Achilles will catch the Tortoise, in 400 seconds
Explanation:
The problem itself reduces the interval of time many times, almost reaching zero. However, if we assume the interval constant, then it is clear that in two hours Achilles already has surpassed the Tortoise (20 miles while the Tortoise only 3).
To calculate the time, we use kinematic expression for constant speed:

The moment that Achilles catch the tortoise is found by setting the same final position for both (and same time as well, since both start at the same time):

Answer:

Explanation:
The motion of ballistic pendulum is modelled by the appropriate use of the Principle of Energy Conservation:

The final velocity of the system formed by the ballistic pendulum and the bullet is:



Initial velocity of the bullet can be calculated from the expression derived of the Principle of Momentum:

