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Alexxx [7]
3 years ago
13

Barack is playing basketball in his back yard. He takes a shot 7.0 m from the basket (measured along the ground), shooting at an

angle of 45 degrees. The ball is 2.0 m off the ground when it leaves his hand, and hits the backboard 3.5 m off the ground. Neglecting air friction, about how long is the ball in flight?
Physics
1 answer:
VMariaS [17]3 years ago
6 0

Answer:

The time of flight of the ball is 1.06 seconds.

Explanation:

Given \Delta x=7\ m

\theta=45 \°

Also, \Delta y=(3.5-2)=1.5\ m

a_x=0\ and\ a_y=-9.81\ m/s^2

Let us say the velocity in the x-direction is v_x and in the y-direction is v_y. And acceleration in the x-direction is a_x and in the y-direction is a_y.

Also, \Delta x\ and\ \Delta y is distance covered in x and y direction respectively. And t is the time taken by the ball to hit the backboard.

We can write v_x=v_0cos(45)\ and\ v_y=v_0sin(45). Where v_0 is velocity of ball.

Now,

\Delta x=v_x\times t+\frac{1}{2}\times a_x\times t^2\\ \Delta x=v_x\times t+\frac{1}{2}\times 0\times t^2\\\Delta x=v_xt

\Delta x=v_0cos(45)\times t\\7=v_0cos(45)\times t\\\\t=\frac{7}{v_0cos(45)}

Also,

\Delta y=v_y\times t+\frac{1}{2}\times a_y\times t^2\\ 1.5=v_0sin(45)\times \frac{7}{v_0cos(45)}+\frac{1}{2}\times (-9.81)\times(\frac{7}{v_0cos(45)} )^2\\\\1.5=7-\frac{481}{(v_0)^2}\\ \\\frac{481}{(v_0)^2}=5.5\\\\(v_0)^2=\frac{481}{5.5}\\ \\(v_0)^2=87.45\\\\v_0=\sqrt{87.45}=9.35\ m/s.

Plugging this value in

t=\frac{7}{v_0cos(45)}\\ \\t=\frac{7}{9.35\times 0.707}\\ \\t=\frac{7}{6.611}

t=1.06\ seconds

So, the time of flight of the ball is 1.06 seconds.

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A car accelerates uniformly from rest to 24.8 m/s in 7.88 s along a level stretch of road. Ignoring friction, determine the aver
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Answer:

When he weight of the car is 8.55 x 10^{3} N then power = 314.012 KW

When he weight of the car is 1.10 x 10^{4}  N then power =  43.76 KW

Explanation:

Given that

Initial velocity V_{1} = 0

Final velocity V_{2} = 24.8 \frac{m}{s}

Time = 7.88 sec

We know that power required to accelerate the car is given by

P = \frac{change \ in \ kinetic \ energy}{time}

Change in kinetic energy Δ K.E = \frac{1}{2} m (V_{2}^{2} - V_{1}^{2}   )

Since Initial velocity V_{1} = 0

⇒ Δ K.E = \frac{1}{2} m V_{2}  ^{2}

⇒ Power P = \frac{1}{2} \frac{m}{t}  V_{2} ^{2}

⇒ Power P = \frac{1}{2} \frac{W}{g\ t}  V_{2} ^{2}   -------- (1)

(a). The weight of the car is 8.55 x 10^{3} N = 8550 N

Put all the values in above formula

So power P = \frac{1}{2} \frac{8550}{(9.81)\ (7.88)} (24.8) ^{2}

P = 314.012 KW

(b). The weight of the car is 1.10 x 10^{4} N = 11000 N

Put all the values in equation (1) we get

P = \frac{1}{2} \frac{11000}{(9.81)\ (7.88)} (24.8) ^{2}

P = 43.76 KW

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