Time, distance & displacement

In summary: In other words, the time taken to reach the sea.In summary, the stone is thrown horizontally with an initial velocity of 30 m/s from a cliff 45 metres above the sea. If the stone had been dropped vertically, it would have taken 3 seconds to reach the sea. When the stone is thrown horizontally, it takes 3 seconds to reach the sea. The horizontal distance traveled by the stone before hitting the sea is 90 metres. The total displacement of the stone from its original point is 90 metres.
  • #1
blaziken's_charizard
34
0
1. Someone throws a stone horizontally from the top of a cliff and out to the sea. The top of the cliff is 45 metres above the sea. The initial speed of the stone is 30 m/s.

a) if the stone had been dropped vertically, how long would it have taken to reach the sea?

b) when the stone is thrown horizontally, how long does it take to reach the sea?

c) what horizontal distance does the stone travel before hitting the sea?

d) what is the total displacement of the store from it's original point?




2. I will be combining both equations and attempted solutions.


For a) : speed=distance/time
Therefore: s=d/t
st=d
t=d/s
t=45m/30ms
t= 1.5 s?

I am clueless about b, c and d :cry:

Please help

 
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  • #2
Your first answer is incorrect, since you did not include the acceleration due to the Earth's gravity. Also, part (a) says the stone is dropped off the cliff. This implies that the initial velocity is zero. Have you come across the kinematic equations for constant acceleration? http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/1DKin/U1L6a.html [Broken]
 
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  • #3
So:

s=ut + 1/2 at^2

45 = 0*t + (1/2*10) *t^2
45= 0 + 5t^2
45=5t^2
45/5=t^2
9=t^2
square root of 9 = t
therefore: t=3 secs?
 
  • #4
Correct.

Now, for the other parts, you need to split up the motion into horizontal and vertical components. So, for (b) you want the time taken for the stone to reach s=0.
 
  • #5
I don't understand what you mean by 'time taken for the stone to reach s=0.'
 
  • #6
Well, if you take the sea as the origin of your coordinate system, and consider the vertical motion. Then, the time taken for the stone to hit the sea is the time taken for the stone to reach postion y=0.
 

1. What is the difference between time, distance, and displacement?

Time is the measurement of how long it takes for an event to occur. Distance is the measurement of the space between two points, while displacement is the measurement of the change in position from the starting point to the end point.

2. How are time, distance, and displacement related?

Time, distance, and displacement are all related through the concept of speed. Speed is the measure of how fast an object is moving and is calculated by dividing the distance traveled by the time it took to travel that distance. Displacement is also related to distance and time, as it is the final position of an object after it has moved a certain distance for a certain amount of time.

3. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Velocity takes into account both the speed and direction of an object's motion.

4. How is displacement calculated?

Displacement is calculated by subtracting the initial position from the final position of an object. This results in the net change in position or the displacement of the object.

5. How do time, distance, and displacement affect each other in motion?

In motion, time, distance, and displacement are all related. Time affects the distance an object travels, as the longer the time, the greater the distance traveled. Displacement also affects the distance an object travels, as the greater the displacement, the greater the distance traveled. Additionally, the relationship between time and displacement affects an object's speed and velocity, as changes in time or displacement will result in changes in speed and velocity.

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