Time and max. height of stone thrown into air.

In summary, the initial speed of a stone projected vertically upwards is 21.0m/s and the maximum height it will reach can be calculated using s=(v^2-u^2)/2a. The total time it is in the air can be found using t=(v-u)/a. The acceleration due to gravity is -9.8 m/s^2.
  • #1
shannon.leigh
9
0

Homework Statement



"The initial speed of a stone projected vertically upwards is 21.0m/s

a)What is the maximum height it will reach?

b) How long does it take to reach the highest point and what is the total time which it is in the air?"

Relative information:
a=9.8 m/s/s
u=21.0 m/s
v=0 m/s
s=?
t=?

Homework Equations



I'm not sure, but I thought v^2=u^2+2as rearranged to s=(v^2-u^2)/2a might be the equation I need for a) at least, then for b), v=u+at rearranged to t=(v-u)/a.


The Attempt at a Solution



When I attempted, I got

a) s=(v^2-u^2)/2a
s=(0^2-u^2)/2*9.8
=-22.5

b) ?

I know this can't be right, because I don't think the distance can be negative. Could some kind person please, please help me?
 
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  • #2
Acceleration acts downwards, so it is supposed to be -9.8 m/s^2 for the acceleration.
 
  • #3
oooohhhhh :) thankyou !
 

1. What is the relationship between time and maximum height when throwing a stone into the air?

The time and maximum height of a stone thrown into the air are directly proportional. This means that the longer the stone is in the air, the higher it will go. This relationship is described by the equation: h = (1/2)gt^2, where h is the maximum height, g is the acceleration due to gravity, and t is the time in seconds.

2. How does air resistance affect the time and maximum height of a stone thrown into the air?

Air resistance can decrease the maximum height of a stone thrown into the air by slowing it down as it travels. This means that the stone will take longer to reach its maximum height and will not go as high as it would without air resistance. The effect of air resistance can be minimized by throwing the stone with a higher initial velocity.

3. How does the mass of the stone affect its time and maximum height when thrown into the air?

The mass of the stone does not have a significant effect on the time and maximum height when thrown into the air. As long as the stone has the same initial velocity and is thrown at the same angle, it will reach the same maximum height regardless of its mass. However, a heavier stone may take slightly longer to reach its maximum height due to the effects of air resistance.

4. What is the optimal angle for throwing a stone to achieve the maximum height?

The optimal angle for throwing a stone to achieve the maximum height is 90 degrees, which is a straight vertical throw. This means that the stone is thrown straight up into the air with no forward motion. At this angle, the initial velocity is completely converted into vertical velocity, resulting in the maximum height.

5. How can the time and maximum height of a stone thrown into the air be affected by external factors?

The time and maximum height of a stone thrown into the air can be affected by external factors such as air resistance, wind, and elevation. Air resistance and wind can decrease the maximum height, while elevation can affect the acceleration due to gravity. Additionally, factors such as the shape and size of the stone, as well as the strength and angle of the throw, can also affect the time and maximum height.

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