Expression which can be used to calculate the time duration of an object traveled a distance X with velocity and acceleration

A trebuchet was a hurling machine built to attack the walls of a castle under siege. A large stone could be hurled against a wal

Studentka2010 [4]

(a) 18.9 m/s

The motion of the stone consists of two independent motions:

- A horizontal motion at constant speed

- A vertical motion with constant acceleration ( $g=9.8 m/s^2$ ) downward

We can calculate the components of the initial velocity of the stone as it is launched from the ground:

$u_x = v_0 cos \theta = (25.0)(cos 41.0^{\circ})=18.9 m/s\\u_y = v_0 sin \theta = (25.0)(sin 41.0^{\circ})=16.4 m/s$

The horizontal velocity remains constant, while the vertical velocity changes due to the acceleration along the vertical direction.

When the stone reaches the top of its parabolic path, the vertical velocity has became zero (because it is changing direction): so the speed of the stone is simply equal to the horizontal velocity, therefore

$v=18.9 m/s$

(b) 22.2 m/s

We can solve this part by analyzing the vertical motion only first. In fact, the vertical velocity at any height h during the motion is given by

$v_y^2 - u_y^2 = 2ah$ (1)

where

$u_y = 16.4 m/s$ is the initial vertical velocity

$v_y$ is the vertical velocity at height h

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

At the top of the parabolic path, $v_y = 0$ , so we can use the equation to find the maximum height

$h_{max} = \frac{-u_y^2}{2a}=\frac{-(16.4)^2}{2(-9.8)}=13.7 m$

So, at half of the maximum height,

$h = \frac{13.7}{2}=6.9 m$

And so we can use again eq(1) to find the vertical velocity at h = 6.9 m:

$v_y = \sqrt{u_y^2 + 2ah}=\sqrt{(16.4)^2+2(-9.8)(6.9)}=11.6 m/s$

And so, the speed of the stone at half of the maximum height is

$v=\sqrt{v_x^2+v_y^2}=\sqrt{18.9^2+11.6^2}=22.2 m/s$

(c) 17.4% faster

We said that the speed at the top of the trajectory (part a) is

$v_1 = 18.9 m/s$

while the speed at half of the maximum height (part b) is

$v_2 = 22.2 m/s$

So the difference is

$\Delta v = v_2 - v_2 = 22.2 - 18.9 = 3.3 m/s$

And so, in percentage,

$\frac{\Delta v}{v_1} \cdot 100 = \frac{3.3}{18.9}\cdot 100=17.4\%$

So, the stone in part (b) is moving 17.4% faster than in part (a).

4 0

4 years ago

Somebody please....

Dmitry [639]

Answer: 12 m/s

Explanation:

6 0

3 years ago

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A solution containing 10.0 g of an unknown liquid and 90.0 g water has a freezing point of -3.33 °C. Given Kf = 1.86 °C/m for wa

Fantom [35]

Answer:

62.06 g/mol

Explanation:

We are given that a solution containing 10 g of an unknown liquid and 90 g

Given mass of solute = $W_B$ =10 g

Given mass of solvent= $W_A$ =90 g

$k_f=1.86^{\circ}C/m$

Freezing point of solution =-3.33 $^{\circ}$ C

Freezing point of solvent = $0^{\circ}$ C

Change in freezing point =Depression in freezing point

=Freezing point of solvent - freezing point of solution=0+3.33= $3.33^{\circ}$

$\Delta T_f=\frac{W_B\times K_f\times 1000}{W_A\times M_B}$

$M_B=\frac{10\times 1.86\times 1000}{3.33\times 90}$

$M_B=62.06 g/mol$

Hence, molar mass of unknown liquid is 62.06g/mol.

6 0

3 years ago

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PLEASE HELPPPPPP <333

Pavlova-9 [17]

Answer:

B. As gravity increases weight increases and as gravity decreases weight decreases

Explanation:

Option B is the correct answer.

From the information given, we can deduce that as the gravity increases, the weight also increases and as the gravity decreases, the weight decreases as well.

This is true from the given table. On earth, the gravity of the man was 9.8m/s² and his weight 588N. But get to space, moon precisely, the gravity reduced to 1.62m/s². Then we discover that such decrease in his gravity also led to the sharp decrease in the weight. The weight decreased from 588N on earth to 96N on the moon.

This actually reveals that weight and gravity are related in a way. Weight of an object is known to be the force of gravity on the object. The weight actually vary as a result of varying gravity.

4 0

3 years ago

The communications system has evolved greatly in the last 20 years. People are now able to communicate more quickly and easily u

Leya [2.2K]

Answer:

Explanation:

transportation might be affected if there's an increase of populatio in canada

3 0

3 years ago

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