give answer in 2 step with explanation at the end of each step and final answer at the end:Problem 4.
Parts (i) and (ii) are independent
(i) An airplane begins ts takeoff run on the runway at point

Question

give answer in 2 step with explanation at the end of each step and final answer at the end:Problem 4.
Parts (i) and (ii) are independent
(i) An airplane begins ts takeoff run on the runway at point A with a speed of 36 km/h and a
constant acceleration a. Knowing that it will take off 25s later at point B and that the distance
AB is 950m. (a) determine the acceleration a in m/s2. (b) determine the take-off velocity Ve in
Km/h
(if) A ball is thrown from the top of a 20m high tower. It has an initial velocity Ve= 10 m/s in the
direction indicated. (a) Determine the x and y coordinates of the point of impact with the ramp.
(b) Determine the velocity of the ball when it hits the ramp.
Les parties (i) et (ii) sont indépendantes.
(Un avion commence son parcours de décollage sur la piste au point A avec une vitesse de
36 km/h et une accélération constante a. Sachant qu'il décollera 25 s plus tard au point B et
que la distance AB est de 950 m. (a) Déterminer I'accélération a en m/s?. (b) Déterminer la
vitesse de décollage Vs en km/h.
(ii) Une balle est lancée depuis le sommet d'une tour de 20m de haut. Elle a une vélocité
initial vo=10m/s dans la direction indiquée. (a) Déter

VIPSolutions · Accepted Answer

## Solution to Problem 4

Let's solve **part (i) step-by-step**, as requested.

---

### **Step 1: Find the acceleration $ a $ in m/s²**

#### **Given:**
- Initial velocity, $ v_ = 36 $ km/h $ = 10 $ m/s (since $ 36 $ km/h $ \times \frac{100}{360} = 10 $ m/s)
- Distance, $ s = 950 $ m
- Time, $ t = 25 $ s

#### **Use kinematic equation:**
$$
s = v_ t + \frac{1}{2} a t^2
$$
$$
950 = (10)(25) + \frac{1}{2} a (25)^2
$$
$$
950 = 250 + \frac{1}{2} a \cdot 625
$$
$$
950 - 250 = 312.5 a
$$
$$
700 = 312.5 a
$$
$$
a = \frac{700}{312.5} = 2.24 \text{ m/s}^2
$$

**Explanation:**  
We used the kinematic equation for uniformly accelerated motion to solve for $ a $.

---

### **Step 2: Find the take-off velocity $ V_B $ in km/h**

#### **Use the equation:**
$$
v = v_ + a t
$$
$$
v_B = 10 + (2.24)(25) = 10 + 56 = 66 \text{ m/s}
$$

Convert $ v_B $ to km/h:
$$
v_B = 66 \text{ m/s} \times \frac{360}{100} = 237.6 \text{ km/h}
$$

**Explanation:**  
We used the first equation of motion to find the final velocity at take-off and converted it to km/h.

---

## **Final Answers:**

- **(a) Acceleration $ a = 2.24 $ m/s²**
- **(b) Take-off velocity $ V_B = 237.6 $ km/h**

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