A particle is thrown horizontally from the top of a tower 80 m high with speed 10 m/s. How long does it take to hit the ground? (g = 10 m/s²)
A. 4 s
B. 2 s
C. 8 s
D. 16 s
Answer (2)
The particle takes 4 seconds to hit the ground after being thrown horizontally from the top of an 80 m high tower. This is calculated using the formula for free fall under the influence of gravity. Therefore, the answer is A. 4 s.
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To determine how long it takes for the particle to hit the ground, we'll focus on the vertical motion of the particle. The problem states that the particle is thrown horizontally, which means the initial vertical velocity is 0 m/s.
The vertical motion can be described by the following kinematic equation:
s = u t + 2 1 a t 2
Where:
s is the vertical distance (80 m, since the tower is 80 m high),
u is the initial vertical velocity (0 m/s),
a is the acceleration due to gravity (10 m/s²), and
t is the time in seconds.
Plugging in the values:
80 = 0 ⋅ t + 2 1 × 10 × t 2
This simplifies to:
80 = 5 t 2
Solving for t 2 , we divide both sides by 5:
t 2 = 5 80 t 2 = 16
Taking the square root of both sides gives:
t = 16 = 4
Thus, the time it takes for the particle to hit the ground is 4 seconds.
So, the correct answer is A. 4 s .
