Projectile motion involves analyzing the trajectory of an object launched into the air under the influence of gravity. In this study, we explore various scenarios such as divers dropping from heights, balls propelled upward, and objects launched at specific angles. Key parameters include initial velocity, launch angle, and vertical acceleration. Using kinematic equations and calculus, we can determine the time of flight, horizontal range, and the velocity of an object at impact. This set of problems provides practical applications of vertical and horizontal motion equations in both metric and imperial units, emphasizing the integration of mathematical models with physical phenomena.
رقم الاختبار1223
الصفالصف الثاني عشر المتقدم
المادةرياضيات
الفصلالفصل الثالث
السنة الدراسية2025/2026
عدد الأسئلة18
إجمالي النقاط18
تاريخ الإضافة2026-05-08
الزيارات142
المعلم
Mr. Ali Abdalla Elbasry
الناشرAmal Salman
يرجى الانتباه إلى أن المعلم قام بإعداد الأسئلة فقط، ولم يقم بإعداد الإجابات أو الشروحات المرفقة. وقد تم توليد الإجابات باستخدام تقنيات الذكاء الاصطناعي، لذلك قد تتضمن بعض الأخطاء أو عدم الدقة.
للحصول على الإجابات الصحيحة والمضمونة، يُرجى الرجوع إلى المعلم أو المصدر الدراسي المعتمد.
السؤال 1
النقاط: 1
A diver drops from a height of 64 feet. Which of the following gives the initial conditions?
Using \(v^2 = v_0^2 + 2g\Delta h\) with v0 = 0, g = 32 ft/s2, and \(\Delta h = 64 \text{ ft}\): \(v = \sqrt{2 \cdot 32 \cdot 64} = \sqrt{4096} = 64 \text{ ft/s}\).
السؤال 3
النقاط: 1
Identify the initial condition y(0) and \(y'(0)\) for the vertical motion, if the object is thrown at a velocity of 6 m/s from a height of 30 m. (Take the origin to be the ground)
The initial height is 30 m above the ground, so y(0) = 30. Since it is thrown upward with a velocity of 6 m/s, the initial vertical velocity \(y'(0) = 6\).
السؤال 4
النقاط: 1
For an object moving in two dimensions shown in figure below. What is the initial value of the vertical component of the velocity?
The vertical component of velocity is calculated using the sine of the launch angle: \(v_{0y} = v_0 \sin(\theta) = 110 \sin(60^\circ) = 110 \cdot \frac{\sqrt{3}}{2} = 55\sqrt{3}\).
السؤال 5
النقاط: 1
For an object moving in two dimensions shown in figure below. What is the vertical acceleration?
An object is launched at angle \(\theta = \frac{\pi}{3}\) radians from the horizontal with an initial speed of 98 m/s. Which of the following give the horizontal range?
Using the equation \(h(t) = -\frac{1}{2}gt^2 + v_0t + h_0\) with g = 32 ft/s2, v0 = 0, and h0 = 30, we get h(t) = -16t2 + 30.
السؤال 10
النقاط: 1
A ball is propelled straight upward from the ground with initial velocity 64 ft/s. Ignoring air resistance, determine the amount of time the ball spends in the air.
Total time in air \(T = \frac{2v_0}{g} = \frac{2 \cdot 64}{32} = \frac{128}{32} = 4 \text{ s}\).
السؤال 11
النقاط: 1
A certain not-so-wily coyote discovers that he just stepped off the edge of a cliff. Four seconds later, he hits the ground in a puff of dust. How high in meters was the cliff?
Using \(h = \frac{1}{2}gt^2\) in meters (g = 9.8 m/s2): h = 0.5 × 9.8 × 42 = 4.9 × 16 = 78.4 m.
السؤال 12
النقاط: 1
The coyote's next scheme involves launching himself into the air with an Acme catapult. If the coyote is propelled vertically from the ground with initial velocity 19.6 m/s, find an equation for the height of the coyote at any time t.
Using \(h(t) = -\frac{1}{2}gt^2 + v_0t + h_0\) with g = 9.8 m/s2, v0 = 19.6, and h0 = 0: h(t) = -4.9t2 + 19.6t.
السؤال 13
النقاط: 1
The coyote's next scheme involves launching himself into the air with an Acme catapult. If the coyote is propelled vertically from the ground with initial velocity 19.6 m/s, find his maximum height.
Max height occurs when v = 0, which is at t = v0/g = 19.6/9.8 = 2 s. Substituting into the height equation: h(2) = -4.9(22) + 19.6(2) = -19.6 + 39.2 = 19.6 m.
السؤال 14
النقاط: 1
A baseball pitcher releases the ball horizontally from a height of 6 ft with an initial speed of 130 ft/s. Find the height of the ball when it reaches home plate 60 feet away.
Horizontal time t = x/v_x = 60/130 = 6/13 s. Vertical position y(t) = -16t2 + 6. So, \(y(6/13) = -16(6/13)^2 + 6 = -16(36/169) + 6 = -576/169 + 6 \approx -3.408 + 6 = 2.592 \text{ ft}\).
السؤال 15
النقاط: 1
A plane at an altitude of 256 feet want to drop supplies to a specific location on the ground. If the plane has a horizontal velocity of 100 ft/s, how far away from the target should the plane release the supplies in order to hit the target location?
First, find the time to hit the ground: \(0 = -16t^2 + 256 \rightarrow 16t^2 = 256 \rightarrow t^2 = 16 \rightarrow t = 4 \text{ s}\). The horizontal distance D = v_x × t = 100 × 4 = 400 ft.
السؤال 16
النقاط: 1
An object is launched from the ground at an angle \(\theta = 20^\circ\) with an initial speed of 48 m/s. Find the time of the flight? (ignore the air resistance)
If we use g = 32 (implied by the options despite the m/s unit), \(T = 2v_0 \sin(\theta)/g = 2(48)\sin(20^\circ)/32 = 96 \cdot 0.342 / 32 = 1.026 \text{ s}\).
السؤال 17
النقاط: 1
One of the authors has a vertical 'jump' of 20 in. What is the initial velocity required to jump this high?
Using v2 = v02 - 2gh, at max height v = 0. h = 20/12 = 5/3 ft. \(v_0 = \sqrt{2 \cdot 32 \cdot 5/3} = \sqrt{320/3} \approx 10.33 \text{ ft/s}\).
السؤال 18
النقاط: 1
A diver drops from 120 feet above the water (about the height of divers at the Acapulco Cliff Diving competition). What is the diver's velocity at impact?
إليك اختبارات إضافية لـ الصف الثاني عشر المتقدم بحسب الفصل الثالث والمادة رياضيات
لا يتم عرض هذا الجزء إلا عند النزول إليه، لتخفيف تحميل الصفحة.
...
🍪
إشعار ملفات تعريف الارتباط
يستخدم هذا الموقع ملفات تعريف الارتباط لتحسين تجربة التصفح وقياس الأداء وعرض المحتوى بشكل أفضل.
باستخدامك للموقع فإنك توافق على استخدامنا لها وفق
سياسة الخصوصية.
