Projectile motion in 2D A projectile is launched from the edge of a cliff, at a height yo above the underlying plateau. The initial velocity vector V=V₂₁ ²+ VyoĴ makes an angle = 45° with respect to the horizontal, as shown in the figure. The projectile lands at a distance from the bottom of the cliff. Find the vebuity vyo as a function of X=xel yo and yog makes this possible. that 9. لم YA L We obtain: 1-95 AG X = = = (1+11+20) A few algebraic steps: Xa-1 =√1+2a Vy = / Yog X2²-2X2+1=X+22 Xα = 2(x+1) d = 2 = 275 yo 34 Newton's II law with constant force (10) Equation of motion: md=-mg )= V dt m → Vx=V₂0, X(t) = √₂+ dvy m мон o-ng - Yo Yongt, утунцаћи де dt. dv₁ = 0 dt The projectile touches ground at time t= ta such that 0=yo+vyotg Vyeo ± √ V 24 Vy g² g = (-sign rejected as it gives to <0). Therefore: XG = V Yoyo (1+1/1+ 2002) g Now use =V₂ (for 9=45°) and introduce and d = X = 26 yo Numbers: while Input parameters are y. and X= 7₂/9₁, g=9.8 m/s². To make things simple, choose X = 2 Yog Then = 2400 m/s² vz Vyo = 40 The three component of this vector equation as 5

A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?

The coordinates of a particle in a rectangular coordinate system are (1.0,4.0,6.0) . What is the position vector of the particle?

A soccer goal is 2.44 m high. A player kicks the ball at a distance 10 m from the goal at an angle of 25 . The ball hits the crossbar at the top of the goal. What is the initial speed of the soccer ball?

A cyclist traveling southeast along a road at 15 km/h feels a wind blowing from the southwest at 25 km/h. To a stationary observer, what are the speed and direction of the wind?

Mt. Asama, Japan, is an active volcano. In 2009, an eruption threw solid volcanic rocks that landed 1 km horizontally from the crater. If the volcanic rocks were launched at an angle of 40 with respect to the horizontal and landed 900 m below the crater, (a) what would be their initial velocity and (b) what is their time of flight?

In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2500 m, climbing at 100 above the horizontal, and moving 30 north of west. The DC-3 is at an altitude of 3000 m, climbing at 50 above the horizontal, and cruising directly west. (a) Find the position vectors of the planes relative to the control tower. (b) What is the distance between the planes at the moment the air traffic controller makes a note about their positions?

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, and she is blown along the following straight lines: 2.50 km and 45.0 north of west, then 4.70 km and 60.0 south of east, then 130 km and 25.0 of west, then 5.10 km due east, then 1.70 km and 5.00 east of north, then 7.20 km and 55.0 south of west, and finally 2.80 km and 10.0 north of east. Use the analytical method to find the resultant vector of all her displacement vectors. What is its magnitude and direction?

What do vectors and scalars have in common? How do they differ?

The F-35B Lighting II is a short-takeoff and vertical landing fighter jet. If it does a vertical takeoff to 20.00-rn height above the ground and then follows a flight path angled at 30 with respect to the ground for 20.00 km, what is the final displacement?