A stone is thrown horizontally from the top of a vertical wall with a velocity of 15m/s hit the horizontal ground at a point 45m from the base of the wall.calculate the height of the wall g=10
You know the rock is falling for 3 seconds. Why? (the horizontal speed is constant)
So, how far does it fall in 3 seconds?
h = 1/2 at^2
To find the height of the wall, we can use the kinematic equation for horizontal motion:
Distance = Velocity × Time
In this case, the stone is thrown horizontally, so its initial vertical velocity is 0 m/s. We can use the equation of motion for vertical motion:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time²)
Since the stone falls vertically, we know that the time it takes to hit the ground is the same as the time it takes for the stone to travel horizontally.
First, let's find the time it takes for the stone to travel horizontally:
Distance = Velocity × Time
45 m = 15 m/s × Time
Time = 45 m / 15 m/s = 3 s
Now, let's find the height of the wall:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time²)
Since the initial vertical velocity is 0 m/s, the equation simplifies to:
Distance = 0.5 × Acceleration × Time²
Distance = 0.5 × 10 m/s² × (3 s)²
Distance = 0.5 × 10 m/s² × 9 s²
Distance = 45 m
Therefore, the height of the wall is 45 meters.
To solve this problem, we can use the basic equations of motion for projectile motion. We know that the stone was thrown horizontally, so its initial vertical velocity (Vy) is zero. We also know that the acceleration due to gravity (g) is 10 m/s^2.
First, let's calculate the time it takes for the stone to hit the ground. We can use the equation:
h = Vyt + (1/2)gt^2
Since the vertical velocity (Vy) is zero, the equation simplifies to:
h = (1/2)gt^2
Where h is the height of the wall and t is the time it takes for the stone to hit the ground.
Now, we need to calculate t. We know that the horizontal distance traveled by the stone is 45 m, and the initial horizontal velocity (Vx) is 15 m/s. Since the stone was thrown horizontally, Vx remains constant throughout the motion.
We can use the equation:
d = Vxt
Where d is the horizontal distance traveled and t is the time taken.
Substituting the given values, we have:
45 m = 15 m/s * t
Simplifying, we find:
t = 45 m / 15 m/s
t = 3 seconds
Now that we know the time it takes for the stone to hit the ground (t = 3 seconds), we can plug this value into the equation for height:
h = (1/2)gt^2
h = (1/2) * 10 m/s^2 * (3 s)^2
h = (1/2) * 10 m/s^2 * 9 s^2
h = 45 meters
Therefore, the height of the wall is 45 meters.