To determine the maximum range covered by the stone, we need to find the height at which the velocity becomes zero (at the highest point of its trajectory). At this point, the stone will start to fall back down.
Using the equation of motion for vertical projectile motion:
v_f = v_i - g*t,
where:
v_f = final velocity (0 m/s at the highest point)
v_i = initial velocity (20 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time
Rearranging the equation,
0 = v_i - g*t,
g*t = v_i,
t = v_i / g.
Substituting the given values,
t = 20 / (-9.8),
t ≈ -2.04 s.
Since time cannot be negative in this context, we'll take the absolute value:
t = 2.04 s.
The total time for the stone to reach the highest point and come back down is twice the time taken to reach the highest point:
total time = 2 * t,
total time = 2 * 2.04,
total time ≈ 4.08 s.
To find the maximum range, we multiply the total time by the horizontal component of the initial velocity:
range = total time * v_i,
range = 4.08 * 20,
range ≈ 81.6 m.
Therefore, the maximum range covered by the stone is approximately 81.6 meters.
A stone is catapulted vertically upward with an initial velocity of 20m/s what maximum range does it cover
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