A person throws a bottle into dustbin at the same height as he is 2 m away at an angle of 45 degrees the velocity of thrown is?

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As you recall, the range of such a trajectory is

v^2/g sin2θ

now just plug in your numbetrs and solve for v

To determine the velocity of the bottle when it is thrown into the dustbin at an angle of 45 degrees, we can use the principles of projectile motion.

As per the given information, the bottle is thrown at the same height as the person (assumed to be ground level) and is located 2 meters away from the person.

In projectile motion, we can break down the initial velocity of the object into its horizontal and vertical components. The horizontal component is the velocity at which the object travels along the ground, and the vertical component is the velocity at which the object moves vertically.

To find the initial velocity, we need to find the horizontal and vertical components and then combine them using basic trigonometry.

1. Horizontal component:
The horizontal velocity remains constant throughout the motion since there are no horizontal forces acting on the bottle (no air resistance in this case). Therefore, the horizontal component of the velocity will be the same as the initial horizontal velocity.

Given that the bottle is thrown 2 meters away, the horizontal component of the velocity can be calculated using the formula:

horizontal velocity (Vx) = distance (d) / time (t)

Since there is no time provided in the question, we assume it takes the bottle the same time to reach the dustbin vertically as it takes to travel horizontally. Therefore, we can use the formula for horizontal velocity without considering time:

Vx = d

Vx = 2 meters

2. Vertical component:
The vertical component of the velocity is affected by gravity since the bottle is in free fall vertically. At its highest point, the vertical component of the velocity will be zero, and at the lowest point (when it reaches the dustbin), it will be equal to the initial vertical velocity.

The formula to calculate the initial vertical velocity (Vy) when the object is launched at an angle is:

Vy = V * sin(angle)

Given that the angle is 45 degrees, and we need to find the initial velocity (V), we can rearrange the formula:

V = Vy / sin(angle)

Since we don't know the value of Vy yet, we can find it using the formula for the time it takes for an object to reach its maximum height in vertical motion:

time to reach maximum height = Vy / g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Using the value of time to reach maximum height, we can find Vy:

Vy = g * time to reach maximum height

First, let's find the time to reach maximum height:
time to reach maximum height = Vy / g = 0 (at maximum height, Vy = 0) / 9.8 m/s^2 = 0 seconds

Thus, the time it takes to reach the maximum height is zero.

Using this information, we can deduce that the only vertical component of the velocity is the initial vertical velocity.

Vy = 0 m/s

Now, substituting the known values into the formula for V:

V = Vy / sin(angle) = 0 / sin(45 degrees) = 0 m/s

Therefore, the velocity of the bottle when thrown into the dustbin at a height equal to the person's height, 2 meters away, at an angle of 45 degrees is 0 m/s.

This implies that the bottle is not thrown horizontally with any velocity component, and it simply falls directly into the dustbin due to gravity.