A ball is shot lip an incline plane with an intial velocity
of , the incline plane has iriclination of . Calculate
(a) maximum distance travelled
(a) Time taken to do this souiney
c) Time of Light

Ask by Garrett Carroll. in Ghana

Mar 17,2025

Question

A ball is shot lip an incline plane with an intial velocity
of , the incline plane has iriclination of . Calculate
(a) maximum distance travelled
(a) Time taken to do this souiney
c) Time of Light

Ask by Garrett Carroll. in Ghana

Mar 17,2025

UpStudy AI · Accepted Answer

To solve this problem, we will break it down into three parts: calculating the maximum distance traveled along the incline, the time taken to reach this distance, and the total time of flight.

### Given Data:
- Initial velocity, $$ v_0 = 40 \, \text{m/s} $$
- Incline angle, $$ \theta = 25^\circ $$
- Acceleration due to gravity, $$ g = 10 \, \text{m/s}^2 $$

### Step 1: Maximum Distance Traveled Along the Incline

The maximum distance $$ d $$ traveled along the incline can be calculated using the formula for projectile motion along an incline:

$$
d = \frac{v_0^2 \sin(2\theta)}{g \cos^2(\theta)}
$$

### Step 2: Time Taken to Reach Maximum Distance

The time $$ t $$ taken to reach the maximum distance can be calculated using the formula:

$$
t = \frac{v_0 \sin(\theta)}{g \cos(\theta)}
$$

### Step 3: Total Time of Flight

The total time of flight $$ T $$ can be calculated using the formula:

$$
T = \frac{2 v_0 \sin(\theta)}{g}
$$

Now, let's calculate each of these values step by step.

1. **Calculate the maximum distance $$ d $$**.
2. **Calculate the time taken $$ t $$**.
3. **Calculate the total time of flight $$ T $$**.

Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(40\sin\left(\frac{25\pi }{180}\right)\right)}{\left(10\cos\left(\frac{25\pi }{180}\right)\right)}$$
- step1: Remove the parentheses:
  $$\frac{40\sin\left(\frac{25\pi }{180}\right)}{10\cos\left(\frac{25\pi }{180}\right)}$$
- step2: Reduce the fraction:
  $$\frac{40\sin\left(\frac{5\pi }{36}\right)}{10\cos\left(\frac{25\pi }{180}\right)}$$
- step3: Reduce the fraction:
  $$\frac{40\sin\left(\frac{5\pi }{36}\right)}{10\cos\left(\frac{5\pi }{36}\right)}$$
- step4: Reduce the fraction:
  $$\frac{4\sin\left(\frac{5\pi }{36}\right)}{\cos\left(\frac{5\pi }{36}\right)}$$
- step5: Rewrite the expression:
  $$4\tan\left(\frac{5\pi }{36}\right)$$
Calculate or simplify the expression $$ (2 * 40 * \sin(25 * \pi / 180)) / 10 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(2\times 40\sin\left(\frac{25\pi }{180}\right)\right)}{10}$$
- step1: Remove the parentheses:
  $$\frac{2\times 40\sin\left(\frac{25\pi }{180}\right)}{10}$$
- step2: Reduce the fraction:
  $$\frac{2\times 40\sin\left(\frac{5\pi }{36}\right)}{10}$$
- step3: Multiply the terms:
  $$\frac{80\sin\left(\frac{5\pi }{36}\right)}{10}$$
- step4: Reduce the fraction:
  $$8\sin\left(\frac{5\pi }{36}\right)$$
Calculate or simplify the expression $$ (40^2 * \sin(2 * 25 * \pi / 180)) / (10 * \cos(25 * \pi / 180)^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(40^{2}\sin\left(\frac{2\times 25\pi }{180}\right)\right)}{\left(10\cos\left(\left(\frac{25\pi }{180}\right)^{2}\right)\right)}$$
- step1: Remove the parentheses:
  $$\frac{40^{2}\sin\left(\frac{2\times 25\pi }{180}\right)}{10\cos\left(\left(\frac{25\pi }{180}\right)^{2}\right)}$$
- step2: Reduce the fraction:
  $$\frac{40^{2}\sin\left(\frac{5\pi }{18}\right)}{10\cos\left(\left(\frac{25\pi }{180}\right)^{2}\right)}$$
- step3: Reduce the fraction:
  $$\frac{40^{2}\sin\left(\frac{5\pi }{18}\right)}{10\cos\left(\left(\frac{5\pi }{36}\right)^{2}\right)}$$
- step4: Factor the expression:
  $$\frac{10^{2}\times 4^{2}\sin\left(\frac{5\pi }{18}\right)}{10\cos\left(\left(\frac{5\pi }{36}\right)^{2}\right)}$$
- step5: Reduce the fraction:
  $$\frac{10\times 4^{2}\sin\left(\frac{5\pi }{18}\right)}{\cos\left(\left(\frac{5\pi }{36}\right)^{2}\right)}$$
- step6: Simplify:
  $$\frac{10\times 4^{2}\sin\left(\frac{5\pi }{18}\right)}{\cos\left(\frac{\left(5\pi \right)^{2}}{36^{2}}\right)}$$
- step7: Simplify:
  $$\frac{160\sin\left(\frac{5\pi }{18}\right)}{\cos\left(\frac{\left(5\pi \right)^{2}}{36^{2}}\right)}$$
- step8: Transform the expression:
  $$160\sin\left(\frac{5\pi }{18}\right)\sec\left(\frac{\left(5\pi \right)^{2}}{36^{2}}\right)$$
### Results of the Calculations

1. **Maximum Distance Traveled Along the Incline $$ d $$**:
   $$
   d \approx 124.82 \, \text{m}
   $$

2. **Time Taken to Reach Maximum Distance $$ t $$**:
   $$
   t \approx 1.87 \, \text{s}
   $$

3. **Total Time of Flight $$ T $$**:
   $$
   T \approx 3.38 \, \text{s}
   $$

### Summary of Results
- **Maximum Distance Traveled**: $$ \approx 124.82 \, \text{m} $$
- **Time Taken to Reach Maximum Distance**: $$ \approx 1.87 \, \text{s} $$
- **Total Time of Flight**: $$ \approx 3.38 \, \text{s} $$

If you have any further questions or need additional calculations, feel free to ask!
Maximum distance traveled: approximately 124.82 meters Time taken to reach maximum distance: approximately 1.87 seconds Total time of flight: approximately 3.38 seconds

A ball is shot lip an incline plane with an intial velocity
of , the incline plane has iriclination of . Calculate
(a) maximum distance travelled
(a) Time taken to do this souiney
c) Time of Light

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Latest Physics Questions

A ball is shot lip an incline plane with an intial velocity of , the incline plane has iriclination of . Calculate (a) maximum distance travelled (a) Time taken to do this souiney c) Time of Light

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

Given Data:

(a) Maximum Distance Travelled:

Summary of Answers:

preguntas relacionadas

Latest Physics Questions

A ball is shot lip an incline plane with an intial velocity
of , the incline plane has iriclination of . Calculate
(a) maximum distance travelled
(a) Time taken to do this souiney
c) Time of Light