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Range of a projectile with time of fligh...

Range of a projectile with time of flight 10 s and maximum height 100 m is : `(g= -10 m//s ^2)`

A

200 m

B

125 m

C

100 m

D

Data incoorect

Text Solution

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The correct Answer is:
To solve the problem of finding the range of a projectile given the time of flight and maximum height, we can follow these steps: ### Step 1: Identify the given values - Time of flight (T) = 10 seconds - Maximum height (H) = 100 meters - Acceleration due to gravity (g) = -10 m/s² (we will use the positive value for calculations, g = 10 m/s²) ### Step 2: Use the time of flight to find the vertical component of the initial velocity The formula for the time of flight (T) of a projectile is given by: \[ T = \frac{2u \sin \theta}{g} \] Rearranging this formula to find \( u \sin \theta \): \[ u \sin \theta = \frac{gT}{2} \] Substituting the known values: \[ u \sin \theta = \frac{10 \times 10}{2} = 50 \text{ m/s} \] ### Step 3: Use the maximum height to find the vertical component of the initial velocity The formula for maximum height (H) of a projectile is given by: \[ H = \frac{(u \sin \theta)^2}{2g} \] Substituting the known values: \[ 100 = \frac{(u \sin \theta)^2}{2 \times 10} \] This simplifies to: \[ 100 = \frac{(50)^2}{20} \] Calculating the right side: \[ 100 = \frac{2500}{20} = 125 \] This indicates a contradiction since the calculated maximum height (125 m) does not match the given maximum height (100 m). ### Step 4: Conclusion Since the calculated maximum height exceeds the given maximum height, there seems to be an inconsistency in the problem statement. Therefore, we cannot determine the range accurately based on the provided values. ### Final Answer The range cannot be determined as the given maximum height does not match the calculated maximum height based on the time of flight. ---
To solve the problem of finding the range of a projectile given the time of flight and maximum height, we can follow these steps: ### Step 1: Identify the given values - Time of flight (T) = 10 seconds - Maximum height (H) = 100 meters - Acceleration due to gravity (g) = -10 m/s² (we will use the positive value for calculations, g = 10 m/s²) ### Step 2: Use the time of flight to find the vertical component of the initial velocity ...
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