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Projectile Thrown Vertically
A small metal ball is thrown vertically upwards with an initial speed of 20ms-1.  
Assuming that air resistance is negligible, calculate  
i)  the time taken by the ball to reach its highest point  
ii) the maximum height reached  
iii) the height, h1.5 of the ball 1.5s after it was thrown  
iv) the speed, v4 of the ball 4s after it was thrown.  
 
If we take upwards to be positive then remember that g will have a negative value in the calculations  
   
i) At maximum height, the speed is zero.  
Therefore we have v = 0, u = 20ms-1 and g = -9.8ms-2  
Rearranging the equation which defines acceleration, we have  
 
 
Therefore, time to reach maximum height = 2.04s  
   
ii) The average value, va of the speed of the ball is  
 
so the distance moved, h, in time t is given by  
 
Therefore the maximum height reached by the ball is h = 20.4m  
   
iii) We will use the equation:  
however, again remember that in this situation, we have defined upwards as positive  
 
Therefore the height of the ball at t = 1.5s is h1.5 = 18.98m  
   
iv) Here we will use the equation:  
again remembering that in this situation, we have defined upwards as positive  
 
This answer tells us that 4 seconds after the ball was thrown, its speed was v4 = 19.2ms-1  
The negative sign tells us that it was moving downwards.  
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