3)A soldier throws a grenade horizontally from the top of a cliff. Which of the following curves best describes the path taken by the grenade?

Parabola

4)A stone is thrown horizontally from the top of a 25.00-m cliff. The stone lands at a distance of 40.00 m from the edge of the cliff. What is the initial horizontal velocity of the stone?

15.60 m/s

3) parabola is correct

4) time of fall = sqrt (2H/g) = 2.26 s
horizontal travel = 40 = 2.26 * V
V = 17.7 m/s

3:

Parabola would be an acceptable choice.

4:
I did not get the same answer as you.

To find the initial horizontal velocity of the stone, we can use the formula:

Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time^2)

In this case, the stone is thrown horizontally, which means its initial vertical velocity is zero, and there is no vertical acceleration. Therefore, the formula becomes:

Horizontal distance = Initial horizontal velocity × Time

Given that the stone lands at a distance of 40.00 m from the edge of the cliff and falls for a height of 25.00 m, we can use this information to find the time it takes for the stone to fall:

Height = (0.5 × Acceleration × Time^2)
25.00 m = (0.5 × 9.8 m/s^2 × Time^2)

Solving for Time:
Time^2 = (25.00 m × 2) / (9.8 m/s^2)
Time^2 = 5.10 s^2
Time ≈ 2.26 s

Now, we can use the time the stone takes to fall to find the initial horizontal velocity:

40.00 m = Initial horizontal velocity × 2.26 s
Initial horizontal velocity = 40.00 m / 2.26 s
Initial horizontal velocity ≈ 17.70 m/s

Therefore, the initial horizontal velocity of the stone is approximately 17.70 m/s.

To answer these questions, we need to understand the concept of projectile motion. Projectile motion refers to the motion of an object that is launched into the air and is subject only to the force of gravity and any resistance caused by the medium it is traveling through.

3) When a soldier throws a grenade horizontally from the top of a cliff, the path of the grenade will follow a parabolic curve. This is because the horizontal motion of the grenade is unaffected by gravity, while the vertical motion is influenced by it. The combination of these two motions results in a parabolic trajectory.

4) To find the initial horizontal velocity of the stone thrown horizontally from the cliff, we can use the following equation:

Range (R) = Initial horizontal velocity (Vx) * Time of flight (t)

R represents the range, which is the horizontal distance covered by the stone.

In this case, we are given the range (R) as 40.00 m. The stone is thrown horizontally from the top of a cliff, meaning the initial vertical velocity (Vy) is zero. As a result, the time of flight (t) can be calculated using the formula:

t = 2 * (height / acceleration due to gravity)^0.5

In this case, the height is given as 25.00 m, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.

Plugging in these values, we can calculate the time of flight:

t = 2 * (25.00 / 9.8)^0.5
t ≈ 2 * 2.551
t ≈ 5.102 seconds

Now we can substitute the range and time of flight into the equation to find the initial horizontal velocity (Vx):

40.00 = Vx * 5.102

Rearranging the equation to solve for Vx:

Vx = 40.00 / 5.102
Vx ≈ 7.83 m/s

Therefore, the initial horizontal velocity of the stone is approximately 7.83 m/s.