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zmey [24]
3 years ago
13

With what speed must a ball be thrown vertically up in order to rise to a maximum height of 45m? And for how long will it be in

air?
Physics
1 answer:
Leno4ka [110]3 years ago
4 0

1) 29.7 m/s

We can solve the first part of the problem by using the law of conservation of energy. In fact, the initial kinetic energy when the ball is thrown from the ground will be entirely converted into gravitational potential energy as the ball reaches its maximum heigth, so we can write:

\frac{1}{2}mv^2 = mgh

where

m is the mass of the ball

v is the initial speed

g is the acceleration of gravity

h is the maximum height

Re-arranging the equation:

v=\sqrt{2gh}

and substituting:

g = 9.8 m/s^2

h = 45 m

We find

v=\sqrt{2(9.8)(45)}=29.7 m/s

2) 6.0 s

First of all, we can calculate how long the ball takes to reach the maximum height. This can be done by using the equation:

v=u+at

where

v = 0 is the final speed of the ball, when it is at its maximum height

u = 29.7 m/s is the initial speed

a = -g = -9.8 m/s^2 is the acceleration of gravity (negative because it is downward)

t is the time

Solving for t,

t= \frac{v-u}{a}=\frac{0-29.7}{-9.8}=3.0 s

So the ball takes 3.0 s to reach the maximum heigth. The time it takes to fall down again is equal, so also 3.0 s, so the total time of the motion is

t = 3.0 + 3.0 = 6.0 s

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Answer:

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Explanation:

Given data

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Put all the values in above formula we get

\tan \theta = \frac{60^{2} }{(150)(9.81)}

\tan \theta = 2.446

\theta = 67.76 °

Therefore the value of  the correct angle of banking for the road is \theta = 67.76 °

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Hi there!

A.

Since the can was launched from ground level, we know that its trajectory forms a symmetrical, parabolic shape. In other words, the time taken for the can to reach the top is the same as the time it takes to fall down.

Thus, the time to its highest point:
T_h = \frac{T}{2}

Now, we can determine the velocity at which the can was launched at using the following equation:
v_f = v_i + at

In this instance, we are going to look at the VERTICAL component of the velocity, since at the top of the trajectory, the vertical velocity = 0 m/s.

Therefore:
0 = v_y + at\\\\0 = vsin\theta - g\frac{T}{2}

***vsinθ is the vertical component of the velocity.

Solve for 'v':
vsin(\alpha_0) = g\frac{T}{2}\\\\v = \frac{gT}{2sin(\alpha_0)}

Now, recall that:
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Plug in the expression for velocity:
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B.

We can use the same process as above, where T' = 2T and Th = T.

v = \frac{gT}{sin(\alpha _0)} }\\\\W = \frac{1}{2}M(\frac{gT}{sin(\alpha _0)})^2\\\\\boxed{W = \frac{Mg^2T^2}{2sin^2(\alpha _0)}}

C.

The work done in part B is 4 times greater than the work done in part A.

\boxed{\frac{W_B}{W_A} = \frac{4}{1} = 4.0}

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