An object projected vertically upward from ground level returns to Earth in 26 seconds. Find the initial velocity in feet per second.

a) 19.6 ft/s
b) 38.2 ft/s
c) 9.8 ft/s
d) 78.4 ft/s

Question

High School

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Answer :

varlord varlord · Answer 1 · 2023-09-28T11:10:14-04:00

The initial velocity of the object is approximately 417.6 feet per second. None of the option is the answer.

Here's how to find the initial velocity of the object:

Recognize equal times for upward and downward motion: Since the object reaches its highest point and falls back to the ground, the time it spends going up is equal to the time it spends coming down (assuming negligible air resistance). In this case, the total time (26 seconds) is divided equally between the upward and downward motion.
Half-time for upward motion: Therefore, the time for the upward motion is t_up = 26 seconds / 2 = 13 seconds.
Kinematics equation with final velocity: During the upward motion, the object reaches its maximum height and then stops momentarily (final velocity becomes 0).

We can use the following kinematic equation:

v_f = v_i - a*t

where:

v_f is the final velocity (0 m/s in this case)

v_i is the initial velocity (what we want to find)

a is the acceleration due to gravity (approximately -9.81 m/s² or -32.2 ft/s²) since it acts downwards (negative sign)

t is the time (13 seconds)

Solve for initial velocity:

Plugging in the known values:

0 = v_i - (-32.2 ft/s²) * 13 seconds

v_i = 32.2 ft/s² * 13 seconds

v_i = 417.6 ft/s (approximately)

Therefore, the initial velocity of the object is 417.6 feet per second. None of the option is the answer.