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iris [78.8K]
3 years ago
7

A ball is launched with an initial velocity of 3m/s, at an angle of 40 degrees above the horizontal, and from a height of 0.5m.

How far will it travel horizontally before it hits the ground?
Physics
1 answer:
Brut [27]3 years ago
6 0

Answer:

The ball travels <u>1.31 m horizontally</u> before hitting the ground.

Explanation:

Given:

Initial velocity of the ball is, u=3\ m/s

Angle of projection is, \theta=40\ degree

Initial height of the ball is, y_0=0.5\ m

Final height of the ball is, y=0\ m

Now, horizontal  and vertical components of initial velocity are given as:

u_x=u\cos\theta\\\\u_y=u\sin\theta

Plug in the given values and find u_x\ and\ u_y. This gives,

u_x=3\ m/s\times \cos(40)\\\\u_x=2.3\ m/s\\\\u_y=3\ m/s\times \sin(40)\\\\u_y=1.9\ m/s

Now, there is acceleration due to gravity acting in the vertical direction. The direction is downward. So, g=-9.8\ m/s^2.

Now, using equation of motion in the vertical direction, we have:

y-y_0=u_yt+\frac{1}{2}a_y t^2

Plug in the given values and solve for time 't'. This gives,

0-0.5=1.9t-0.5\times 9.8\times t^2\\\\-0.5=1.9t-4.9t^2\\\\4.9t^2-1.9t-0.5=0

On solving the above quadratic equation, we get:

t=0.57\ s\ or\ t=-0.18\ s

Ignoring the negative result as time can't be negative. So, time taken by the ball to reach the ground is 0.57 s.

Now, as the ball moves, there is no force acting on it in the horizontal direction. So, the acceleration in the horizontal direction is 0.

Now, we know that, when acceleration is zero, the body moves with a constant speed.

Hence, distance traveled in the horizontal direction is given as:

Horizontal distance = Horizontal component of initial velocity × Time

R=u_x\times t

Plug in the given values and solve for 'R'. This gives,

R=2.3\times 0.57\\\\R=1.31\ m

So, the ball travels 1.31 m horizontally before hitting the ground.

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Answer:

The semi truck travels at an initial speed of 69.545 meters per second downwards.

Explanation:

In this exercise we see a case of an entirely inellastic collision between the semi truck and the car, which can be described by the following equation derived from Principle of Linear Momentum Conservation: (We assume that velocity oriented northwards is positive)

m_{S}\cdot v_{S}+m_{C}\cdot v_{C} = (m_{S}+m_{C})\cdot v (1)

Where:

m_{S}, m_{C} - Masses of the semi truck and the car, measured in kilograms.

v_{S}, v_{C} - Initial velocities of the semi truck and the car, measured in meters per second.

v - Final speed of the system after collision, measured in meters per second.

If we know that m_{S} = 2200\,kg, m_{C} = 2000\,kg, v_{C} = 45\,\frac{m}{s} and v = -15\,\frac{m}{s}, then the initial velocity of the semi truck is:

m_{S}\cdot v_{S} = (m_{S}+m_{C})\cdot v -m_{C}\cdot v_{C}

v_{S} = \frac{(m_{S}+m_{C})\cdot v - m_{C}\cdot v_{C}}{m_{S}}

v_{S} = \left(1+\frac{m_{C}}{m_{S}} \right)\cdot v - \frac{m_{C}}{m_{S}} \cdot v_{C}

v_{S} = v +\frac{m_{C}}{m_{S}}\cdot (v-v_{C})

v_{S} = -15\,\frac{m}{s}+\left(\frac{2000\,kg}{2200\,kg} \right) \cdot \left(-15\,\frac{m}{s}-45\,\frac{m}{s}  \right)

v_{S} = -69.545\,\frac{m}{s}  

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Answer:

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Explanation:

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