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In-s [12.5K]
2 years ago
7

If a ball is dropped off a tall building and accelerates at 9.8 m/s^2 until reaching the ground at a speed of 55 m/s, how long w

ill it take for the ball to reach the ground?
Physics
1 answer:
bearhunter [10]2 years ago
8 0

Answer:

5.61s

Explanation:

\pink{\frak{Given}}\begin{cases} \textsf{ A ball is dropped off a tall building and accelerates at 9.8 m/s$^2$ .}\\\textsf{It reaches the ground at a speed of 55 m/s .} \end{cases}

And we need to find out the time taken by the ball to reach the ground .

  • The initial velocity of the ball will be 0 since it is dropped .

Here we can use the First equation of motion , namely ;

\sf \longrightarrow v = u + at

where the symbols have their usual meaning . Now substituting the respective values , we have,

\sf \longrightarrow 55m/s = 0m/s + 9.8 m/s^2(t)\\

\sf \longrightarrow 55m/s = 9.8m/s^2(t)\\

\sf \longrightarrow t = \dfrac{55m/s}{9.8m/s^2}\\

\sf \longrightarrow \boxed{\bf time = 5.61 s }

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A person takes a trip, driving with a constant speed of 94.5 km/h except for a 22.0 min rest stop. If the person's average speed
qwelly [4]
From the average speed you can fix an equation:

Average speed = distance / time

You know the average speed = 65.1 kg / h, then

65.1 = distance / total time,

where total time is the time traveling plus 22.0 minutes

Call t the time treavelling and pass 22 minutes to hours:

65.1 = distance / [t + 22/60] ==> distance = [t + 22/60]*65.1

 
From the constant speed, you can fix a second equation

Constant speed = distance / time traveling

94.5 = distance / t ==> distance = 94.5 * t

The distance is the same in both equations, then you have:

[t +22/60] * 65.1 = 94.5 t

Now you can solve for t.

65.1t + 22*65.1/60 = 94.5t

94.5t - 65.1t = 22*65.1/60

29.4t = 23.87

t = 23.87 / 29.4

t  = 0.812 hours

distance = 94.5 km/h * 0.812 h = 76.7 km

Answers: 1) 0.81 hours, 2) 76.7 km


4 0
3 years ago
Which graph accurately shows the relationship between kinetic energy and speed as speed increases?
mixer [17]

Answer:

B

Explanation:

kinetic energy (KE) is the energy possessed by moving bodies. It can be expressed as:

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

Where: m is the mass of the object, and v its speed.

For example, a stone of mass 2kg was thrown and moves with a speed of 3 m/s. Determine the kinetic energy of the stone.

Thus,

KE =  \frac{1}{2} x 2 x 3^{2}

     = 9

KE = 9.0 Joules

Assume that the speed of the stone was 4 m/s, then its KE would be:

KE =  \frac{1}{2} x 2 x 4^{2}

     = 16

KE = 16.0 Joules

Therefore, it can be observed that as speed increases, the kinetic energy increases. Thus option B is appropriate.

3 0
3 years ago
A child, hunting for his favorite wooden horse, is running on the ground around the edge of a stationary merry-go-round. The ang
olga55 [171]

Answer:

9.22 s

Explanation:

One-quarter of a turn away is 1/4 of 2π, or π/2 which is approximately 1.57 rad

Let t (seconds) be the time it takes for the child to catch up with the horse. We would have the following equation of motion for the child and the horse:

For the child: s_c = \omega_ct = 0.233t

For the horse: s_h = s_0 + a_ht^2/2 = 1.57 + 0.0136t^2/2 = 1.57 + 0.0068t^2

For the child to catch up with the horse, they must cover the same angular distance within the same time t:

s_c = s_h

0.233t = 1.57 + 0.0068t^2

0.0068t^2 - 0.233t + 1.57 = 0

t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

t= \frac{0.233\pm \sqrt{(-0.233)^2 - 4*(0.0068)*(1.57)}}{2*(0.0068)}

t= \frac{0.233\pm0.11}{0.0136}

t = 25.05 or t = 9.22

Since we are looking for the shortest time we will pick t = 9.22 s

6 0
3 years ago
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