Acceleration due to gravity/velocity questions (I've done the work)

In summary: in summary, the student can throw the pen up with an initial speed of 3.8m/s, it will take 0.736735m for it to reach its maximum height, and it will take 0.775510s for it to reach the ground.
  • #1
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I'm having trouble with these 2 questions. I've tried them and come up with solutions but would like someone to check if I have done them properly.

A traditional watch has a second hand 1.5 cm long from the center to the tip.

a) What is the speed of the tip of the second hand?

d = 2Pir
d = 2(3.14)(1.5)
v = d/t
v = 2(3.14)(1.5)/60s
v = 0.157 cm/s

b) what is the velocity of the tip at 15s? 45s? 60?

0.157 cm/s (right)
0.157 cm/s (left)
0.157 cm/s (up)

c) What is the change in velocity between 30s and 45s?

I'm having trouble with this one. Do I use the pythagorean theorem because one is pointing to the left and one is pointing down.

0.157^2 + 0.157^2 - sq root
v = 0.222 cm/s (sw)

A student tosses their pen vertically upward with an intial velocity of 3.8 m/s.

a) Maximum height

Vf^2 = Vi^2 + 2ad
0 = 3.8^2 + 2(-9.8)d
d = 0.736735 m

b) How much time will pass before the pen returns to his hand if it is at the same level that he released the pen at?


d = v2t - 1/2at^2
0= (3.8)(t) - 1/2(9.8)t^2
t = 0.775510 s

c) if the student's hand is 1.5 m above the ground and he misses the pen, with what speed will the pen hit the ground.

0.736735 + 1.5 = 2.236735 m

Vf^2 = Vi^2 + 2ad
Vf^2 = (0) + 2(9.8)(2.236735)

vf = 6.62117 m/s (down)

Can someone please check these over. I would really appreciate it. Thank you.
 
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  • #2
1b you have the positions not the velocity. When the hand is at 15s=3 O'clock, which direction is it moving in?
 
  • #3
mgb_phys said:
1b you have the positions not the velocity. When the hand is at 15s=3 O'clock, which direction is it moving in?

clockwise?

Are the other questions correct?
 
  • #4
1a is correct.
1b draw a diagram and put an arrow for the direction the hand is moving - is it moving up/down/left/right?
1c, correct but possibly by accident. Draw a diagram with the speed in x and y-axis and the overall speed is the hypotenuse of the triangle

2a correct
2b correct you could also do v=u+at for the upward path and then double the time.
2c you can also use the fact that it arrives back at the hand with the same speed it was thrown up with. So it's the same as throwing it down with an initial speed of 3.8m/s
 
  • #5
mgb_phys said:
1a is correct.
1b draw a diagram and put an arrow for the direction the hand is moving - is it moving up/down/left/right?
1c, correct but possibly by accident. Draw a diagram with the speed in x and y-axis and the overall speed is the hypotenuse of the triangle

2a correct
2b correct you could also do v=u+at for the upward path and then double the time.
2c you can also use the fact that it arrives back at the hand with the same speed it was thrown up with. So it's the same as throwing it down with an initial speed of 3.8m/s

Thank you so much I really appreciate it :)
 

What is acceleration due to gravity?

Acceleration due to gravity is the rate at which an object falls toward the Earth due to the force of gravity. It is measured in units of meters per second squared (m/s²).

How is acceleration due to gravity calculated?

The acceleration due to gravity can be calculated using the formula g = GM/r², where G is the universal gravitational constant, M is the mass of the Earth, and r is the distance between the object and the center of the Earth.

What is the velocity of a falling object due to gravity?

The velocity of a falling object due to gravity can be calculated using the formula v = gt, where g is the acceleration due to gravity and t is the time elapsed. This formula assumes that the object is falling in a vacuum, with no air resistance.

How does the acceleration due to gravity change on different planets?

The acceleration due to gravity varies on different planets depending on their mass and radius. For example, the acceleration due to gravity on the surface of the Moon is about one-sixth of the acceleration on Earth.

Can the acceleration due to gravity be negative?

Yes, the acceleration due to gravity can be negative. This occurs when an object is moving in the opposite direction of the gravitational force, such as when it is thrown upwards or when it reaches the top of its trajectory during free fall.

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