Chapter 6: Q 121. (page 383)

The projectile is fired at an angle of 45° to the horizontal with an initial speed of $100$ per second. Find the range R and maximum height H.

Short Answer

Expert verified

The range R is $31 \cdot 05$ and height H is $0 \cdot 77$ .

Step by step solution

Step 1. Given information.

Consider the given value the initial speed is $100$ feet per sec and $θ = 45 °$ .

Step 2. Formula used.

The formula used to find range is.

$R (θ) = \frac{{ν_{o}}^{2} \sin 2 θ}{g}$ and formula to find height is $H (θ) = \frac{{ν_{o}}^{2} \times {(\sin θ)}^{2}}{2 g}$ .

Step 3. Finding range and height.

Substitute the values in formula where $ν_{o}$ is 100 and $θ$ is $45 °$ and $g = 9 \cdot 8$ .

$R (θ) = \frac{{ν_{o}}^{2} \sin (2 θ)}{g} R (θ) = \frac{{(100)}^{2} \sin (2 \times 45 °)}{9 \cdot 8} R (θ) = 31 \cdot 05$

Further simplify.

$H (θ) = \frac{100 \times {(\sin θ)}^{2}}{2 g} H (θ) = \frac{100 \times {(\frac{1}{\sqrt{2}})}^{2}}{2 \times 9 \cdot 8} H (θ) = 0 \cdot 776$

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The projectile is fired at an angle of 45° to the horizontal with an initial speed of $100$ per second. Find the range R and maximum height H.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used.

Step 3. Finding range and height.

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The projectile is fired at an angle of 45° to the horizontal with an initial speed of 100per second. Find the range R and maximum height H.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used.

Step 3. Finding range and height.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Mechanics Maths

Discrete Mathematics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The projectile is fired at an angle of 45° to the horizontal with an initial speed of $100$ per second. Find the range R and maximum height H.