What is the length of a string with a mass of 2.5 kg, with a

A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the hori

EastWind [94]

Answer:

the child is 1.581 m far from the fence

Explanation:

The diagrammatic illustration that give a better view of what the question denote can be seen in the image attached below.

From the image attached below, let assume that the release point is the origin, then equation of the motion (x) is as follows:

$x - x_o = u_xt$

$\mathtt{x = u_xt \ \ \ since (x_o = 0)}$ ---- (1)

the equation of the motion y is :

$\mathtt{y - y_o =u_yt - 0.5 gt^2}$

$\mathtt{y = u_yt-4.9t^2 \ \ \ since (y_o =0)}$

$\mathtt{ 1= (u \ sin 40^0)t -4.9 \ t^2 }$

$\mathtt{1 = 8 sin 40^0 t - 4.9 t^2}$

$\mathtt{1 = 5.14t - 4.9t^2}$

$\mathtt{4.9t^2 - 5.14t +1 = 0}$

By using the quadratic formula, we have;

$\mathtt{ \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a}} }$

where;

a = 4.9, b = -5.14 c = 1

$= \mathtt{ \dfrac{ -(-5.14) \pm \sqrt{(-5.14)^2 - 4(4.9)(1)}}{2(4.9)}} }$

$= \mathtt{ \dfrac{ 5.14 \pm \sqrt{26.4196 -19.6}}{9.8}} }$

$= \mathtt{ \dfrac{ 5.14 \pm \sqrt{6.8196}}{9.8}} }$

$= \mathtt{ \dfrac{ 5.14+ \sqrt{6.8196}}{9.8} \ \ OR \ \ \dfrac{ 5.14- \sqrt{6.8196}}{9.8}} }$

$= \mathtt{ \dfrac{ 5.14+ 2.6114}{9.8} \ \ OR \ \ \dfrac{ 5.14- 2.6114}{9.8}} }$

$= \mathtt{ \dfrac{ 7.7514}{9.8} \ \ OR \ \ \dfrac{ 2.5286}{9.8}} }$

$= \mathbf{ 0.791 \ \ OR \ \ 0.258} }$

In as much as the ball is traveling upward, then we consider t= 0.258sec.

From equation (1)

$\mathtt{x = u_x(0.258)}$

$\mathtt{x = ucos 40^0 (0.258)}$

$\mathtt{x = 8 \ cos 40^0 (0.258)}$

$\mathbf{x = 1.581 \ m}$

Thus, the child is 1.581 m far from the fence

6 0

3 years ago

A heavy ball with a weight of 100 NN is hung from the ceiling of a lecture hall on a 4.4-mm-long rope. The ball is pulled to one

allochka39001 [22]

Answer:

175.3 N

Explanation:

The motion of the ball is a uniform circular motion, therefore the net force on it must be equal to the centripetal force.

There are two forces acting on the ball at the lowest point of motion:

- The tension in the string, T , upward

- The weight of the ball, $mg$ , downward

The net force (centripetal force) has the same direction as the tension (upward, towards the centre of the circular path), so we can write:

$T-mg=m\frac{v^2}{r}$

where the term on the right is the expression for the centripetal force, and where:

T is the tension in the string

$mg=100 N$ is the weight of the ball

$m=\frac{mg}{g}=\frac{100}{9.8}=10.2 kg$ is the mass of the ball

v = 5.7 m/s is the speed of the ball at the lowest point

r = 4.4 m is the length of the rope, so the radius of the circle

Solving for T, we find the tension in the string:

$T=mg+m\frac{v^2}{r}=(100)+(10.2)\frac{5.7^2}{4.4}=175.3 N$

7 0

3 years ago

The graph below represents the relationship between speed and time for an object moving along a straight line. What is the total

KiRa [710]

The distance travelled by the object during the first 4 seconds is 80 m

<h3>Definition of speed </h3>

Speed is defined as the distance travelled per unit time. Mathematically, it can be expressed as:

Speed = distance / time

With the above formula, we can obtain the distance travelled by the object in the first 4 seconds.

<h3>How to determine the distance travelled </h3>

Speed = 20 m/s
Time = 4 s

Distance =?

Speed = distance / time

20 = distance / 4

Cross multiply

Distance = 20 × 4

Distance = 80 m

Complete question:

See attached photo

Learn more about speed:

brainly.com/question/680492

4 0

3 years ago

How is velocity different from speed?

enyata [817]

Velocity, unlike speed, includes a direction.

Velocity is a vector quantity which is defined by magnitude and direction.

Speed is a scalar quantity. It is the rate at which an object moves regardless of which direction.

5 0

3 years ago

Read 2 more answers

40 Points!!!!!!!

marshall27 [118]

D. Ted associated being asked a question with embarrassment.

7 0

3 years ago

Read 2 more answers